> 1. Right now, anyone can register at a tikiwiki site. Can we and how do we moderate the registrations?
See at "Admin (click!)> Login", and select there the options you desire (validate users, keyword needed, etc.), or you can just allow everybody to register and login, and allow very minim permissions to registered, and create a new group registered_plus, to allow more permissions to this new group.
And moderate manually the subscripction to the new group, etc.
> 2. Can administrators grant blog creation rights to registered users? How to do so?
Yes, check "permissions" and "user and group management" (search documentation for this issue or related)
Hope it helps.