There's not that much that is unsuitable for piggies as in "Should Never Eat" but there are lots that should only be given in moderation. > 
Allergies are a nightmare- my DD gets a rash but no breathing problems , from our previous boar (Rex) and our present boar (Teddy) but she's fine with a friends Teddy (or I wouldn't have got a coarse coat) but she's "Meh, rash". it doesn't affect her as a asthmatic allergy would (poor DH)
The cat litter we use is from The Range, big yellow bags, it has on the bag "Suitable for rabbits/rodents" and I've seen rabbits cages with this bedding but they are tidy and litter trained, unlike hogs.
We have 2 sows and a boar. The sows pee loads.
Newspaper takes 90% then I pick the grubby bits of litter.
Easiest way to insulate the cage outside is put it on a piece of cardboard under the cage. I wedge cardboard round the back of the haybox for ours.
You can easily change it or add if you need to.
A layer of cardboard in the base of the cage too? No staples or tape though.
It is a tough decision with Piggie. If he was mine, I would get him a new mate (we matched an adult with a baby, ) then you have a never ending cycle of pigs (We said our girls were last, but we are really pleased we got GP6 boar)
At school , he'll get all the noise and chat.
If you take him for weekends, he'll cope with the journey I;m sure, and he'll get to know his house at yours.
But it depends on your DH, if he can cope.
My pigs come in for winter nights (in Nov) and I am constantly sweeping up hay which can be as much an allergen as the pig fur.