During a Time Capsule 35 Pass Erase, do I have to keep my computer on / running?
The The Time capsule doesn't need your Mac to run. Once it receives the wipe command, it will run to completion without needing anything but power from the all. (Ok - you could cancel the erase or it could error out, but in most cases the erase completes on its own accord.) You also don't need a Mac to start the wipe command. Airport Utility runs on Windows and iOS as well.