Yes. When you put things in the crate, it fills up a white bar at the bottom of the crate UI. Once the white bar is full, so is the crate.
Also make sure sure to take attachments off any weapons or they'll disappear over restart/ log out
Yeah, in that case I'd say they should try fishing or excavating or maybe mining. Mainly things where you have to collect a lot.
They patched this somewhat recently
Escort them to the court house in any main city. You can see where court houses are marked on the map in green text. Once you get there just scroll wheel on them and select send to jail.