1) Does it require C-compiler

From a quick view at the source tar ball, it doesn't look like. Some dependencies might need that, though.

Is it easily portable to different web servers running under different OS

As far as I can tell it uses standard interfaces like CGI, FastCGI or mod_perl. So if your servers support one of those: yes. (Note that plain Catalyst + plain CGI is rather slow, and not recommended)

3) If I created everything on windows how difficult would it be to move to UNIX and to Linux WEB hosts

If you don't mess up the paths it should be quite easy.

4) Will it help me to simplify client programming and web design

I don't know what you mean wiht "client programming". Catalyst is something that works on the server side. As for the web design aspect - it uses templates, so your web designer doesn't need to know any perl.

5) Will it help me to separate business and UI programming for my web application

Yes.

6) Does it have performance issues compared to regular Perl/CGI if my code makes a lot of computations

The biggest hit compared to plain Perl + CGI is the startup time, which you can eliminate by using fastcgi or mod_perl.