Most people just use a NAS (self built or one of the pre-built types) & stuff a bunch of hard drives into it. Or just stuff a bunch of hard drives into their desktop(s).
Sure there are people outfitting rack(s) of server(s) but generally that's just the truly dedicated people going that route.
For what it's worth hard drives nowadays go up to ~22TB so your 34TB example would only need two massive hard drives. A compact NAS or small desktop would work fine for that example.
That sounds correct. AFAIK most countries in the world do not do credit card AVS (address verification service) so aside from a select few countries you would be able to enter just about any address for those country's cards.
e.g. related discussion https://money.stackexchange.com/questions/11979/in-what-countries-can-credit-card-merchants-use-address-verification or just search the internet for other sources.
The one catch is the card would have to be from that country that doesn't support AVS e.g. for India I think you are saying that you used an India based card, right?