Great news that the hog likes the new house! Sounds like a definite seal of approval for your handiwork!
Hogs don’t have families, as in Mum and Dad and children. The Mother is solely responsible for raising the hoglets. The Father probably wouldn’t even know if any hoglets are his – hogs are fairly promiscuous and apparently some litters have even been known to have more than one Father! But there could be a family, as in Mum and hoglets – until the hoglets grow up and go it alone.
I can’t be sure, but one hog on its own using a house for maybe a few days at a time, sounds a bit like a male. Hopefully if he is a big adult hog, the owls will leave him alone. If the owls have always been there and there are still hogs around, it sounds as if the owls aren’t having much impact on them.
The cats shouldn’t bother the hogs – the main problem with them is that they tend to eat the hogs’ food. but a feeding box could help minimise that problem.
Ideally if you want the hog house to be used for nesting (either a birthing nest or a hibernating nest) it’s best not to have the feeding area or box too close to the hog house – because the food may attract predators.
The hog house will probably be ok next to your house, but hogs don’t need to be kept warm for hibernation. Their temperature needs to fall to a certain level for them to be able to reduce their metabolic rate, which is what happens when they hibernate. Ideally they need to build a well insulated nest so that their body temperature doesn’t fluctuate too much. That is best left to the hog – they are excellent at building hibernation nests. So clever!
If you want the hog to use the house for hibernation, the thing to do is to leave lots of suitable material nearby – i.e. don’t tidy up the leaves in your garden too much. (if you want to rake them off a lawn, then you could move them to in amongst the plants in borders). Hogs’ preferred materials are medium sized leaves, long grasses, etc. They are able to layer the leaves together a bit like tiles on a roof, but lots of layers – making a hibernation nest really well insulated. Long grasses help them weave everything together. They leave a small hog sized hole in the middle which they can curl up in.
Good luck and happy hog watching!