WordPress.org

Does this plugin has a per user invitation card limit?

No. Right now it does not, but this feature will come shortly.

On my site the registration possibility is tured off, is it possible to accept a registration card in this case?

Yes. If you invited your friend, and he clicks on the link in the e-mail he/she can register to the blog, even is the registration is not enabled.

Does this plugin works with the latest WordPress ?

Yes, it does :)

What about the older versions?

I'll have to test under them.