Logging (already registered) user through registration form?

1. What comes first registration or login?
2. Should I login after registration?

What comes first registration or login?

Registration only happens the first time you access the system. It is a way to check your credentials. Every time after your initial registration, you will log on to the system using the username and password you created.

Should I login after registration?

It can be safe to auto login if the user already has an active session as the correct user during the confirmation step. If you think about it, it's not actually "automatically logging them in" but simply keeping them logged in as they was before. During all that time, there was no reason to end the session.