please help me

See http://docs.elgg.org/wiki/DuplicateInstallation

What do u mean

I think he means :- "..dont want the entire site like facebook just the profile page."  cannot be answered in just one sentence, because the code effort involved wil most likely will be 100 - 200++ lines of php code in order implement such a feature ;-) Are you ready for that kind of work ?

YEah just tell me which files do I need to copy from the facebook theme and where I need to copy them

You could extend page/elements/head with your code in a plugin.

If something that simple can speed up Elgg, then please report back :-)

The first snippet is already built into Elgg. Caching is handled by Elgg, just make sure you have simplecache enabled.

As for gzip compression, I don't think there is one specific place. You would need to go through all handlers and lib/views and see which ones use ob_start()

have you looked at apache2's mod_deflate instead of mod gzip ?