BuddyPress.org

I have one question

Here are the three answers to your one question!

Is it the case that anyone can register on the community and create a blog

You can control blog registration in WPMU’s backend. Log into the admin panel as site administrator and visit “Site Admin > Options > Allow new registrations”. There are a few settings which give you some basic control.

Can the community admin restrict who has the privilege to do that

If the community admin is the overall site admin, then see the first answer.

is it possible to make membership by invitation only?

http://bp-dev.org/plugins/wpinvites/

Also of potential interest: https://buddypress.org/forums/topic.php?id=1328