User is always registered at the time of purchase. Once they hit they Register button and the registration validates they're stored in the system. It does not matter if purchase was successful or not. There's no fix this other than to manually delete them if the purchase is declined. You can however setup CBSubs to require an active subscription so if they try to login it'll block their account if they don't have a subscription. You can enable this within CBSubs > Settings > Global and disallowing free registrations without a subscription.

No, not currently but CB Privacy has Delete Me and Disable Me fields that in next release moderators will be able to use in addition to the users self. So in next release of CB Privacy you'll have a way, but currently there isn't one without putting something together with CB Auto Actions. Both are going to require a Professional subscription though.

Just to be clear, when the next release of CB privacy rolls out I will have to purchase a professional subscription to gain access?

No, only if you're going to use the CB Auto Actions method. CB Privacy is available to Advanced. So you'd only need an Advanced subscription.

Looks like on the website Advanced subscription will allow me access to CB Privacy.

Correct, sorry; my previous reply was confusing on this matter.

Can I purchase CB Privacy a la carte?

I do not suggest purchasing single purchases. You get absolutely no support for single purchases and you can not use your CBSubs support for an individual purchase. In other words if you could purchase it individually you would be on your own for its usage.

Regarding the question directly I have no idea. Nick sets up the individual purchases and I can't recall which are available.