[crediblewitness]

> - If I buy a TLD, will I own it in perpetuity, even after I die?

No, if you don't send a renewal transaction, the name goes up for auction again.

> - Is this going to have the same environmental problems as Bitcoin, or will having fewer transactions mean that's less of an issue?

Yes, it's proof of work

> I'm not necessarily feeling great about the idea of having separate TLDs for every site

TLD owners manage the namespace as they see fit. that includes issuing/selling/giving away sub-domains. <subdomain>.<TLD namespace>