What does Google login credentials mean, where/when does the phone require me to input it? After I unlock my phone it seems my phone is already logged into Google from the previous login as I can see my Google contacts list without logging in to Google again.
Login credentials means username and password.
Yes, of course you are logged in if you just unlock it. But if the thief can unlock it it's game over: they have access to your data, they can turn off your internet connection so you can do nothing, they can remove your account from the phone. At that point all you can do is notify your service provider and have the phone blacklisted.
But a factory reset wipes you apps and data from the phone. So after a reset your phone is not logged into Google. However, any phone that was released with Android 5 or later stores your login credentials in a separate secure storage device and requires you to re-enter them after a reset. If you can't do that, you can't log in. This is what's called "factory reset protection".
What is the purpose of factory reset by a thief if my phone has password/fingerprint lock? After the factory reset, the phone is still not usable correct, so what is the point of wasting time to factory reset?
A reset will remove the screen lock (PIN/password/whatever). Their purpose is to protect your data, so if the thief reset the phone to get past the screen lock they also removed your data. But they provided no protection to the hardware: if that was what the thief was after then a reset would give them a clean phone that they could log into with a new account use or sell to someone else.
That is why the factory reset protection scheme was introduced, which is entirely separate from the screen lock. Its purpose is to make the phone unusable after a reset unless they know your Google login, and hence make it less attractive to a thief.
A corollary of this is that if you want to sell a phone you should remove your Google account from it before resetting it. Otherwise the buyer won't be able to use it (we get a log of requests for help from people who have bought phones and found them to be FRP locked).
If a phone has password/fingerprint lock, after the thief factory reset, does the phone still has password/fingerprint lock?
No.