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Application web: message sending

I am developing a web application where several clients can send messages to each other, it would be like instant messaging without strong real-time constraint.
To illustrate the situation, let's imagine a classroom where students are on a web page and can send messages to their teacher who is on another web page displaying all the messages.
The teacher can answer questions and therefore the pages of the students who have received answers must update with the respective answer.
The first research of solution are unsuccessful because it turns around form and installation of specific library.
What is the easiest solution to implement?
For information, I am developing with javascript, php and mysql; I have no possibility to modify the server part nor to install libraries.
Thank you.
LG

Get steamID with Steam API using javascript

First off sorry if this question is a 'bad' one; I am very new to the world of web apps, API's and Javascript.
As the title says I am trying to get a user's steamID using the Steam API using javascript.
This is for a web app that needs to get information about the games a user plays. (Which from my understanding is only obtainable using this special ID.)
My initial thoughts on how to do this would be to use openID so that the user gives Steam their info and the ID is returned to my app.
I have seen that there are lots of examples of this using php; however, because of project requirements, everything must be run in the browser. There is no backend server to even run php on so it is not an option what so ever.
I have spent a better part of a day trying to figure this out and have made no real progress, everything seems to lead back to using php. (maybe what I need under my requirements is not possible?) So an example or anything really would be much appreciated.

welcome to Stack Overflow I can see you are confused as to where to start or progress so here is a basic roadmap:
You will need to contact Steam to get an API key first.
Next part is more tricky for a beginner. You will need to get node.js which is a package manager. Effectively it's a large library of javascript programs which you can import into your own program to do things with. One of these so called "packages" is openid-client, which is an implementation of openID that you can add to your site. Users click on the openID button on your site, it redirects them to steam servers, they login, then your site gets their info without leaking their username or password to you.
Now that you have both the steamID and your API Key your program can input these two into the url steam provides to get owned games. You can input this completed url into fetch or axios (another node package that can request data from servers) and it will respond with the user's owned games in json format.
Here are a list of resources in order to get you started:
https://steamcommunity.com/dev
https://nodejs.org/en/
https://www.npmjs.com/package/openid-client
https://www.npmjs.com/package/node-fetch OR https://www.npmjs.com/package/axios
https://developer.valvesoftware.com/wiki/Steam_Web_API#GetOwnedGames_.28v0001.29
I suggest reading the documentation in each of these links and seeing if there is any youtube tutorials that try and do what you are doing with these technologies to help you implement them as a newbie. Overall there is a lot to learn on each of these technologies but as long as you orient yourself using guides or tutorials you will succeed. Good luck.

Check out this page: How to retrieve Steam username using SteamWorks API?.
However, it seems like an issue you might be having is connecting to the actual API. What exactly are you using for testing?
I know from experience, for example, that you can connect using Postman to various API's, and format a request for them in a chosen language, including JS>

Using a server to send/receive information between a mobile phone and web page

I am trying to set up a simple set up as follows:
Have a mobile app with a page consisting of 4 lines (4 html paragraph lines (I am using phonegap)).
I want to use a web page from which I will input the data for those 4 lines. This information is sent to a server and that server transfers this information to that app on that mobile phone. Now, those 4 lines on the mobile phone is filled with the new information.
Similarly user inputs information on another page consisting of 10 lines of li (list). This information is again sent to the server and to the web page where the information is displayed.
I can almost feel the "internet police guys" getting all hyped and ready to vote this question down. But please understand that I have been on this site and various forums desperate to find a tutorial to guide me to do this and not able to find.
I am trying to use ajax to perform this setup. Confused how I would be using the php file. Information such as password n username is going to go in that php file to connect to the server. But php is a server side script thus needs to sit at the public_html folder. How do I use the php file from my desktop? Write a separate javascript to access it?
It is the concept that is confusing me. I am familiar with html,js,php.
I would appreciate any guidance or maybe a link to a tutorial which would help me to do the concept I mentioned. Thanks for listening.

You will need to create an API using PHP. This API is uploaded to your server and is considered "RESTful". Google a tutorial for what fits your needs. You can set all sorts of rules in this API such as requiring any requests to have an ID or access token.
Since you are using PhoneGap, your HTML and JS files rest on the device, so you will need to allow permissions to your API from anywhere. For this you will have to speak to your host provider about unless you know how to configure it yourself (some providers restrict what you want to do by default as an extra security precaution against XSS attacks).
Next, you can either use jQuery, or you can write some AJAX calls by writing the JavaScript yourself.
The most efficient way for this to work is to send JSON objects to and from the API. You will include a "command" in the JSON when you are sending from your app. On the PHP side, you will retrieve this command and use the rest of the data included in your JSON object to process the request. Your API will need to encode a JSON object for return (such as a user's profile information).
Here is a basic PHP API tutorial to get you going that explains some of the features of a RESTful API: PHP API
Here is a simple AJAX function (you will probably want to make this much more modular): AJAX

As broad as your question is, it seems like the best/easiest thing for you to do will be for you to first create a PHP webpage that will access a SQL database to perform the record updating. Actually, this should serve all of your needs for your mobile users assuming you don't need push notifications for live data updates.
I am assuming, since you are using phone gap, that you are more comfortable with web languages. After you get the webpage fully operational, then you should start building your app based on that exact same SQL database. With mobile app development there are a lot more "what if's" (what if the phone rings, what if the app is running in the background, what if there is no cellular service, etc...)
It is always easier to start with what you know and build on that, rather than starting with a new development platform and troubleshooting as problems arise.

Automatic userlist update

I have a online user list which is populated by a SQL query to a database table.
When a new user comes online, how can i make the webpage automatically update?
What code do I need to provide?
Thanks

There are a few ways you could do this, but I'll avoid the most tempting WebSockets HTML5 new-ness and suggest the following:
When a user logs on, record the fact that they are logged on to the database.
From your page, poll a service or web page method that lists online users.
If the list changes, update the part of the page that shows the users.
That's the rough outline of what to do. If you need specifics please say what server-side host and programming language you are using. From the client side, please also mention what JavaScript framework you'd prefer or are open to.

Implementing web chat, how do I get typing status?

Can someone illustrate how I can get typing status of the other party with JavaScript?
UPDATE
Can someone recommend a one-to-one open source chatting application, preferably written in PHP? I only found open source chatting rooms which are for chatting among all onliners, but I just need a one-to-one chatting.

Here are a list of PHP-based open-source instant messaging software.
Some of those might be relevant for you.

For example, if you had an text area #chat then you could use this code to attach the event:
document.getElementById('chat').addEventListener('keydown', FUNCTION HERE, false);

See http streaming and some ready solutions here: http://ajaxpatterns.org/HTTP_Streaming
this is how google talk does it. And there are ready php or c++ solutions
It was quie a discovery for me!

This is an update to reflect the significant change in the OP's question:
Google Chat and Facebook both use XMPP(jabber) servers, as do most companies I know of that have internal instant messaging.
The nice part about XMPP is that you get all of the "is typing" and other presence-based information without having to roll-your-own in javascript (bear in mind, you will still need to use javascript to pass XMPP requests back to the server, but XMPP has most of the features you'd need already built in).
Check out OpenFire. It's a great XMPP server, totally open source, and they have a web-based version of their Spark client that is pretty nice.
Or you could get a PHP library for XMPP (there are a few). But you'd still need to have the XMPP server running in the background for PHP to work with.
Here's a list of XMPP libraries for PHP from XMPP.org:
Eiffel
JAXL
Lightr
Missus
xmpphp
Or, if you want to keep things mostly browser-side, they also have a list of libraries for javascript:
dojox.xmpp
js.io
JSJaC
strophe.js
xmpp4gwt
xmpp4js

I made a small chat application a while ago, and the only way to do it is to frequently check for new entries in the chat database and fetch anything newer than the last displayed message. At the same time as all that, you can check to see if the user's input is empty. If it is, do nothing. If it isn't, enter a status code into the database beside that user's name. If anyone has that status in the database when you're fetching information about new messages and who is online, you should display the 'user is typing' message. I hope that makes sense...let me know if it isn't.

For User1: If you save the chat message on each key-press to the database, with a status: sent=false and update the last updated date.
For User2: you could pole periodically for the presence of a message where sent=false and use the last updated to update user is typing message. if the lastupdated date is more than a say ten seconds you could remove the message as that person may have stopped typing. This will allow User2 to see User1 typing, stopping and continueing again.
Ideally polling for this information will be part of an existing call to the database to reduce additional overhead.