Issues with Messages

Hello,

I know there are hundreds of discussions everywhere about why Messages sometimes doesn't send message to a contact or it says the contact is not registered with Messages, and I am suffering from same craziness. I can send messages from my other Apple devices just fine, and am having these problems on my OSX.

In trying to see what happens, I added my google account to the Messages, and now I cannot delete that or any other account on the Messages.