I have two powerbanks. My smaller one is a 4000mah one ($13) and the longest I've tested it was for 6 hours, and it still had over 75% battery. So it could easily run one for a full day.
You'd have to script it yourself, but I don't see why not. Mine is designed to be fully automatic though, so encrypting it would be pointless.
The range depends on whatever wifi adapter you use. The built in wireless of the Zero W sucks, so you'll only get about sixty feet or so before dropoff. But a good ALFA036NEH with a 9dbi antenna would work much better. It's just however much you want to pay for an antenna, and how small you want it to be.
Extend the range by using a ba=etter wireless adapter/antenna.
Technically sure, but the plastic official raspberry pi case, or even an Altoids can will work just fine.
I've never tested this, it just depends on the capabilities of the device you're using. This is not resource intensive at all. I'd be more worried about network bandwidth before ever worrying about a concurrent user limit.
It has both an imageboard and a fileshare system built in.
Most of these answers are publicly available. Just check the raspberry pi website for the throughput.
This thing and a cellphone battery or two would fit in an aluma wallet. A pelican case sounds like overkill to me.