So far I know that sql and php caching can improve performance. But my question is if is it possible to use caching on sharing host?
Only if the hosting company has made something available to you like one of the PHP caches such as APC etc. otherwise you’re stuck with a half way house of file based caching - which can actually still speed things up considerably (it’s what we do for our own site).
For shared hosting this capability is probably limited without user manipulation allowed. Think about it, you are paying a small amount of money so it shouldn’t really expected of the host to offer this.
If you move up to a VPS, dedicated server, cloud, etc you’ll probably more likely to see this feature.
I believe they are the kind of operations which are issued for the whole server not for the certain account. So what you need is just to find such web hosting company which do that on the whole server.
It is perfectly possible if your host has this feature enabled. Just ask before signing for it. cPanel comes now with eaccelerator as an option in apache and I guess that many will have it
If your PHP and SQL are very intense, it can be faster to just cache a copy of the output as a static file and then to serve that file instead. This is exactly what plugins such as WPSuperCache do for WordPress for example so it’s not something that is new.
What kind of site are you running?