Is it possible to restrict a part of a website to craft user-groups?
For instance if I want show an internal Blog to members-only.
And is it possible to moderate user registrations? So when somebody registers an Admin has to approve it first?
It is! You can use the requirePermission
tag:
{% requirePermission "yourPermission" %}
See the full documentation here. Keep in mind this list as built in permissions but you can also add custom permissions through a plugin should you require it.
As far the second question, I'm not 100% sure but I believe you can set "enabled" to "false" when creating a registration form. See further details here.
Update: You can also use isInGroup