Develop Reference

Code needed for form to talk to phpmyadmin backend

I am creating a search form in wordpress using html and javascript. The form has dropdown menus which will have preselected items. These items come from the phpmyadmin(wordpress backend database). I'm having trouble writing the php code so the form talks to phpmyadmin backend. Does anyone have code for this?

John is right on that. PHP MyAdmin is a web based utility for accessing MySQL similar to WordPress which is a CMS. You will need to make queries to the backend database either directly(Not Advised) or to a web server. Wordpress has support for plugin databases built right in. Just gotta do a couple things.
Per The WordPress Site
Write a PHP function that creates the table.
Ensure that WordPress calls the function when the plugin is activated.
Create an upgrade function, if a new version of your plugin needs to have a different table structure.
WordPress - Creating Tables with Plugins
If you insist on writing it yourself you will need to setup a web server like Apache or nginx to listen to request and execute your PHP scripts.
PHP 5 Form Handling
PHP Connect to MySQL
and if you want to go dynamic
Ajax and JS, but you may want to use PostMan for testing.

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.

Can I use PHP SDK and JAVASCRIPT SDK at the same time?

I have a php program/app which asks for input, generate an image and post th image link to user's timeline (processor.php). I used PHP SDK in posting to timeline since I am more familiar with PHP. Now, in my gallery.php, i want to show like buttons for each generated image. I am aware that i have no option but use JS SDK in making button. but is it fine if i use two different SDK's in a single app?
processor.php - PHP SDK
gallerry.php - JS SDK
thanks for your answer! I would love to try your suggetions too

There shouldn't be any problem using PHP and JS in the same application, quite a common use case. You would normally use PHP to create the Web Application structure, handle backend logic, and then use JS to handle UI events.
There's nothing special about combining the two, just create the Web page with JS as normal for the view, and use PHP to build it.
Hope this helps.

Yes, there is no problem, the two APIs are designed to work together. The PHP API is usually used to created the backend logic (for example OAuth implementation, posting and getting data, etc) and the JS API to handle user iniated events.
Also see this: https://stackoverflow.com/a/6728092/1107118 on how to handle login state. Normally the JS API is used for logging in too, and then with the PHP API you take the access token and do the backend actions.

call live webservice from simple html page...?

I read lots of post here, but don't get specific answer.
I have live server on which I have my web services work properly.
now, I want to create one simple html page through which I call that web service.
with javascript this is possible but what is exact.
I repeat again only html and javascript through which I want to call that web service.

you can use jquery to load the data from webservice, but you might need to include jquery js file and your browser(IE) might prompt for security violation and you might need to click yes.

How to build an interactive Ajax Web Widget?

I am looking to create a web widget that can be easily integrated into any website using javascript and posts a form to my server, returns the data and displays the results appropriately. This will all happend in a small area of the host websites screen, like google adsense. I am aware that this is XSS and also the cross domain issues with ajax.
What I need help with is cementing the flow of such a widget. Has anyone done anything like this before?
The general process is:
Website embeds javascript - external js
Javascript renders a form
User submits form with POST data
POST data is sent to external server
Server responds and updates widget to display tabular data
Is this possible? How could it be achieved? Should I use / avoid using a JS framework such as Prototype / JQUery for this project?
If anyone knows any good tutorial resources for building widgets that would be great.
Any help would be greatly appreciated.

using a library like jQuery is not possible, since you don't know whether the website that uses your widget has the jQUery-library referenced.
If you use an iframe, and show something of your own host, you are able to use a library if I'm not mistaken.