I'm not sure I understood your question properly, but I'll try to answer it based on what I think it means.

What is referred to as Favourites in Internet Explorer is called Bookmarks in Firefox. You can access those by clicking the button to the immediate right of the Star button in the area near the Menu button. If you'd like to set a bookmark for a page you're currently viewing, click the Star button to save it.

If you'd like to access cookies for the site you're viewing, click the icon to the immediate left of the web address you're on and then click "More Information..." in the window that pops up click "View Cookies" and it'll show you all cookies set by that website. If you'd like to see all cookies for all websites click in "X" in the search field found in the previously mentioned window.

Alternatively, click Menu button > Options > Privacy > Firefox will: Use custom settings for history > Show Cookies...

I hope I understood your question properly, otherwise let us know.

I probably didn't explain it very well. I'll try again. First I know how to keep favorites or bookmarks. If I sign into my Verizon homepage and/or email page and check that I want to stay signed in for two weeks (as you can on Verizon), I am able to do this with IE even if I delete my history and cookies because IE also has a place which I have checked which states the following:

 Preserve Favorites website data
Keep cookies and temporary internet files that enable your favorite websites to retain preferences and display faster. 

The above is found when you click on tools in IE and then click on Delete browsing history. On Fire Fox if i check stay signed in for two weeks I am signed out if I delete history and cookies. Hope this explains it. Those in charge of Fire Fox would have to update it with the Preserve Favorites website data option.

Hi,

The people who answer questions here, for the most part, are other Firefox users volunteering their time (like me), not Mozilla employees or Firefox developers.

If you want to leave feedback for Firefox developers, you can go to the Firefox Help menu and select Submit Feedback... or use this link. Your feedback gets collected at http://input.mozilla.org/, where a team of people read it and gather data about the most common issues.

Take a look at this extension - https://addons.mozilla.org/en-US/firefox/addon/self-destructing-cookies/

And if that doesn't meet your needs, see this Cookies search of AMO