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How to Load an external web page inside my one and hide some content (avoiding cross site problems)

I need to incorporate in my web application some content from an external dynamic web page on which I have no control.
Then I need to filter some of the content of this page or to hide it for presenting only the relevant part that is interesting for my use.
I need also that the scripts on the external page are still working on the source site of the loaded content without cross-site protection.
Is all that possible? How can I do it? Any code example, please?
I suppose that this can be made with JS on client side .
I work on back side and these themes are quite extraneous to me, please don't blame me.

No, it is not possible.
Browser same-origin policy is designed to prevent malicious websites from doing evil.
Same-origin Policy restricts JavaScript network access to prevent evil.
Same-origin Policy also restricts script API Access to prevent evil.
From the Docs:
JavaScript APIs like iframe.contentWindow, window.parent, window.open, and window.opener allow documents to directly reference each other. When two documents do not have the same origin, these references provide very limited access to Window and Location objects.
To communicate between documents from different origins, use window.postMessage.
— MDN Web Security Reference - Cross-origin script API access
One can not use <iframe> elements as a way to "avoid cross site problems". The Same Origin Policy was created to protect users from evil web pages.

Determining the iframe parent

I have a web page that will be embedded in iframes on multiple domains. I need to determine which domain is embedding my content.
document.referrer doesn't work, because I need the parent window, not the home page of the site or the page last visited prior to navigating to my page.
I don't have any control over the sites that are embedding my content.

Because of abuse over the years Web-browsers & servers have added security.
One of them being is preventing an iframe from accessing the parent Domain unless it meets the SAME ORIGIN POLICY.
https://en.wikipedia.org/wiki/Same-origin_policy
Now the HOST which your website will be embedded can allow access your to access the parent host. Something called CORS for short.
https://en.wikipedia.org/wiki/Cross-origin_resource_sharing
Also check out.
https://en.wikipedia.org/wiki/Web_Messaging
Hope that answer your question some.

Cross-domain JavaScript iFrame-parent access blocked

I'm designing some "add-on" to certain websites, which should be embedded in them as an iframe. Inside this iframe there is a clickable button aimed at changing the iframe's position within the parent website.
Since things are done in coordination with the parent website, I am able to add some code there as well. However it seems I am not able to do neither of the following (one of them should suffice):
From the iframe, access data within the parent.document, in order to move the iframe to the desired position.
From the parent website, access data within the iframe, in order to check when the button is clicked.
Both typically produce an error: "Blocked a frame with origin XXX from accessing a frame with origin YYY. Protocols, domains, and ports must match".
Any advice (preferably with code sample) is appreciated.

After doing lots of searching around, I came across this:
http://www.codeproject.com/Tips/585663/Communication-with-Cross-Domain-IFrame-A-Cross-Bro
I actually tested the method (using my own short piece of code) and it seemed to work on Chrome, Firefox and IE. Now I'm gonna try the "real" implementation...

From what I understand based on the information you've provided in your question, cross domain scripting is not possible. What you would need to do is provide a script that the parent-level website can paste into their template/html and run from their domain, similar to how Google does with their analytics system.
As an alternative, try turning your iframe content instead, into a div loaded with the response from a service call made from the parent domain to the iframe domain. You would most likely need to create an API that a requesting site can use. Simply call that URI with whatever parameters you would use when referencing the page you wanted to load in the iframe, and have the script that you run on the parent website handle all the DOM alterations you want to achieve.

Cross Domain JavaScript with DHTML HTC's

I have a typical setup for cross domain.
site1.company.com
site2.company.com
Main application is running off of site1.company.com. Trying to get communication working between the a parent frame from site1 and child frame from site2
Both site 1 and site 2 are setting document.domain='company.com';
The communication works fine both ways, However the parent frame from site1 was no longer able to communicate with the rest of the site1 application due to the same origin policy. I added the same document.domain property to every web page in site1.
The issue I am now facing is all of our 20 some HTC files are no longer functioning. I attempted to set the document.domain in the script tag on the HTC's but this threw an access denied message.
Trying to use the HTC's without the document.domain results in the same origin policy failing and HTC javascript calls are throwing access denied.
Is there something special I have to do to enable document.domain in an HTC file? Can this even be done?

Take a look at http://easyxdm.net/, it will enable you to embed frames that you can communicate freely and securely with across the domain boundary.
It will probably be easier than mucking about with document.domain (causes all sorts of issues).
This will most likely not work between HTML and HTC's, but it will between pages on the separate domains.

Getting around same origin policy in javascript without server side scripts

I have an environment that doesn't allow server side scripting really (it is extremely difficult to get a script "installed" on the server). I tried using an iframe to violate javascript's same origin poilcy; however, that didn't work. Are there any other workarounds I am not aware of?
Thanks!

As David Dorward mentioned, JSON-P is the simplest and fastest; however, there is another trick, specifically using two iframes.
Two get around this issue without using JSONP, you can do the following. This technique assumes that you have some sort of development access to the parent page.
There are three pages on two domains/sites.
Parent page
Content page
Cross-domain communication page (aka "xdcomm")
Pages the parent and xdcomm pages are hosted on the same domain, the content page is hosted on any other domain. The content page is embedded as an iframe in the parent page and the xdcomm page is embedded as a hidden iframe in the content page.
The xdcomm page contains a very simple script that detects GET parameters in the query string, parses that string for method and args variables (where args is a JSON encoded string), and then executes the specified method with the specified arguments in the parent page. An example can be seen here (view source).
Even though JavaScript's Same Origin Policy restricts code on one domain from accessing that of another, it doesn't matter if domains are nested within each other (domain A, nested within domain B, nested within domain A).
So, in a nutshell, the content page sends messages to the parent page via the xdcomm page by changing the source of the iframe to something like http://domaina.com/xdcomm.html?src=foo&args=[1,2,3,4]. This would be equivalent to executing foo(1,2,3,4) in the parent page.
Also, know that there are already libraries that help you with this, such as easyxdm. What I've explained here is the basis of one of the techniques that they use, and while it might not be as fancy, it is certainly a fully functioning and lightweight implementation.

Hopefully not, as it would be a security hole! :)
But if both your sites are subdomains on the same domain, maybe document.domain can help.