You are taking different things and making them to mean that which they do not.
Yes, home group is already created. But no, you are not currently in one. I will post a picture of what it looks like if you are part of a homegroup:
The highlighted option "Leave the homegroup..." is how you know you are in one.
Believe me, this is just how it works. It may be different to what you are used to, but that is just the way it is.
The password is what a computer uses to "join" your homegroup (Now remember, it is already created, but no, you are not connected). You can view the password, etc. but you will need the password in order to connect computers together.