My computer runs very slow on internet and other program
Firefox, IE, Chrome, etc are internet browsers, Yahoo isn't. If you meant the page you first see when you open your browser that is called your homepage, and yes you'll be able to use Yahoo as your homepage and email with any browser. It used to be that some sites wouldn't work in Firefox, but that is very rare any more, any major site should work fine. Also just because you install Firefox doesn't mean you won't be able to use IE if you need to, you'll just have the option of Firefox or IE.
Yes, I saw your other thread about CCleaner. I've never used it, but it may help (I wouldn't be worried about it being anything bad).