When I first got mine, I ran it in hot spot mode before I could figure out how to connect to my router. I was a bit disappointed, but I think it was simply a case of too many obstructions. It’ll do fairly well with a good los. 50 ft ish?
I’ve never used anything but ac power, but I understand it works fine in the manner you described.
The fan plugs directly into the guru port, no adapter needed.
Once the unit is powered, it will stay set even if you lose connection, as long as the power to the unit is on. Even if the power goes off and comes back on, it goes to the previous settings.
I still love my controllers, I don’t do long cooks without it.
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