Apologies if this is a dumb question, but I can't quite figure out the answer -
How do I purchase several domains and check out at once instead of having to re-check out every time I want to purchase or renew a domain?
It's just one at a time here. Other registrars may have a bulk-purchase mechanism. If it's worthing registering here, then it's worth the one at a time approach. And that's the last time you'll have to handle registrations one at a time. Renewals can be automatic.