Should I set up Identity Server to use same database as my applications?
If you want to, you can.
How is normal forms registration done when using federated security?
This is up to you and (currently) outside the realm of IdentityServer.
Is it possible to authenticate users from each individual RP(mvc application) and still get SSO without redirecting user to STS?
Not really -- SSO via the browser is all about doing redirects back to the IdP because the user is logged into the IdP via the browser. Only when the IdP is confident of the user's identity will it then issue a token to the RP.
What happens when STS fails? Are users then unable to login to any application? Is there any solution to this?
The STS is a critical part of your enterprise, so you want to do everything you can to ensure it's up.