I just installed 2.2 on my site, do I need to put my license key in the box?

and being a new version, why does the Admin CP say there are updates available?

No on the license key. As far as the updates message, that's coming from Invision's server which is only seeing that you're not running the latest stable version. :)

I see. What about registrations, do I have to disable them?

I don't think so, as there are several public testing boards up right now. I run one myself.