How is it integrated with TOR itself? What if the TOR network goes down one day?
the TOR network is made up lots of Tor nodes, the only way for it to go down is for all the nodes to go down.
Meanwhile, I would be happy if someone could clarify, please: When I'm running a Torcoin Wallet, am I also automatically running a Tor node, thus helping the Tor network? I'm interested in any insights...
Yes if you are running on this branch here >>
https://github.com/TorCoinProject/torcoin/tree/tor