It's unusual for a rescue to give a single guinea-pig. Most will only re-home one if you've got a GP at home (and then you have to 'match' them). That's what makes me think that he might be one of those hogs that really don't get on with company.
Them saying he might get on is taking a risk (I'm assuming they would have tried him with guinea-pig company).
You would either have to neuter him, wait the 'safe' time for him to be strile then find him a girl.
Or get a very young boar piglet (which you might be able to find in a rescue but usually they are older). Then hope that the little boars Terrible Teens aren't too bad (usually 6 months age)
How big is your cage? (there's lots of information on cages in Cavy Cages website). Bigger is definately better, and if you got a 2nd pig you'd have to remove all your Pigs smells to make it 'neutral territory'.
Some GPs are more toothy. Mine will give us a gnaw (not a bite as such, more of a nip.Doesn't break the skin. I don't bother as such but I don't want to encourage it. Usually it's something we've done, like smelling of food, touching them (GP1 greasespot or GP2 right side) that they give a warning)
If he's always been a bitey little s*d that might just be him.
If it's just started, maybe he's trying to tell you he's in pain.
Check his nails, teeth, skin/fur.
The garden will be too wet and cold for him. And it gets dark so early now. He'll be cold and lonely.They aren't hardy like outdoor rabbits.
My boars are in at night (in our small bedroom). They have each other in their Pighouse (wooden Playhouse) and a cuddle and chat in the evening. They go to bed when the DC do.
Can you spend more time with him at Christmas. Get a paddling pool if you can to let him go into the lounge (keeps them safe and they won't pee everywhere). Then your DD can give him a guinea adventure playground with boxes and tunnels.
I can honestly say (apart from when we've been on holiday and they went to Little Animal Boarding) there has not been a day when we've not given the Pigs a cuddle and check up. My DD is completely smitten with her pig.