This might sound a little out there, but regarding the rats, know anyone with a good rat terrier? A good ratter can make short work of rats. If I could have a dog, that's the kind of dog I would have.
As to the termites...
We moved into a house with termites and ants. We rent from a landlord whose idea of success is based on their bank account. Long short, it's our problem not theirs unless we want to waste time and money in court and risk eviction.
We tried a lot of things, I forget them now, because what worked the best was wood chips. I put an unconscionable amount of wood chips in the yard as mulch, for the pathways, to rot as compost. About 30 chipper loads the first two years and about two or three a year since. (We have an acre lot.) The ants and termites moved out of the house and now live happily in the wood chips.
I hesitate to make that recommendation, because what works in one place won't necessarily work in another. It could be they moved out because they'd eaten their fill of the house! Who knows!
As to the fungi, not all fungi is bad. That said, I came across of vile smelling fungi in the yard a few years back, and all the plants in the area looked ill. I ripped out the plants because I didn't want them anyhow, then I drowned the area with hydrogen peroxide. No more fungi.
I forgot to mention, rodents, ants, termites, all sorts of folks we'd rather not have love living under stonework, asphalt, and other hardscape that keeps them safe from predators and harsh weather. I used to think it was stupid to see folks watering their driveways (still do under most circumstances.) Then I learned if I watered the crack in the asphalt, the ants would stay in the ground. If I didn't, they'd come into the house looking for water.
