One sign in for Apple ID across all applications on MacBook

This is possible. You can log out of your Apple TV and have someone else log in. This can get kind of annoying though. But it is possible.

If you have multiple computers in the house though, each with stuff bought with different Apple IDs, and you just want to access the content on the machines, that is very possible too. You can set up home sharing with one Apple ID on your Apple TV and then on the rest of the other machines. It has to be the same ID across the different machines but it will let you access all the computers that are on the network from the Apple TV and access and stream the content stored on them.

You can find a great tutorial over here.

You can still do things the old fashion way and log out and log back in, it can just be kind of tedious. Home Sharing can really simplify the process if you just want to share content from multiple computers though.

does Apple automatically sign out all connected devices when changing your password?

If they are still signed in (at the time you change the password) it will not sign them out, but next time they will have to use the new password to sign in.

Your problem is clearly with someone who cracked your old gmail account.

Now they have created NEW apple id and can verify it since they have access to email.

• go to that gmail and change the password to a strong one.

You only got a copy of that email since you have the forwarding turned on.

You must have created a apple id once upon a time since it is needed for basic service like system software updates.

Your original apple id might be still OK and not compromised (but change the password on it anyway).