It’s very difficult to tell if a bunny wants a friend or not. Most bunnies do, but it has to be the right bunny, and only the bunny knows waht rabbit is the right one. Some shelters offer speed-dating for bunnies for this reason, so the bun can pick a friend himself. That is often very successful, but not available everywhere.
Bringing another bun into your home can result in loss of litter-box habits, because buns are territorial and mark out their territory with poop and pee. This can be a temporary thing or it can be permanent. There’s no way of telling.
Is Finn neutered? He’ll have to be if he is to have a friend. The friend too must be desexed.
Bunnies can form strong bonds with their human, and they can be sad if their human leaves them, but it’s not quite like when they lose a rabbit they’re bonded to. If your mother is prepared to take care of Finn while you are away and she’s willing to give him a chance to love her, I think he’ll be fine without you for a few months.
It’s normal for a bun to take food and run off with it. My Bam does that even when his favorite person in the world (my mother) gives him a treat. Bam can sit in my mothers lap for any amount of time and just doze off while she pets him – but if he’s on the floor when she gives him a treat, he runs off with it. It’s more an instinct than lack of trust, I think. Some dogs does that too, if you give them sth particularly yummy.
Bunnies can be a long time about accepting people. It’s built into their genes to regard non-rabbits as possible predators looking to eat them. A human who wants to bond with a rabbit as a rule needs LOTS of patience.