when my bitcoin core finishes synchronizing does it make my desktop to be like blockchain.nfo where people can create wallets.

and must i be online always.

No.

Bitcoin Core is purely a wallet, mostly for personal use.

When bitcoin core syncs it means it is downloading previous blocks / blocks that have ""happend"" while bitcoin core had no access to internet.

apart from that does it mean i have all the bitcoin history from 2009 till date on my hard drive

Yes. It does mean you have all bitcoin transacations and blocks since 2009 on your computer.

if my hard drive is compromised does it put all the bitcoin core information in my desktop at risk

It shouldn't if you have your wallet encrypted, otherwise, yes.