No, you can only host domain extensions that are accessible on the regular, public internet here. The .onion TLD isn’t a “real” TLD, so you cannot setup a site with it here.
We also don’t have Tor installed on our servers, so I’m not sure how a .onion site would be accessible in the first place. And yes, Tor MUST be installed on the server for this to work, you cannot connect to the Tor network from within a website script.
No, they are free. I’m not sure where you get that pricing from.
.onion domains are addresses on the Tor network. Anonymity and obscurity is pretty much the main purpose of the Tor network, so having to give someone your credit card details and personal information so they can keep a record of all domains registered and their owners kinda defeats the purpose.