Precautions for a subterranean level

My home is built on a slight slope and my shop (attached) is partially earth sheltered, it has about 4.5' stem walls. To ensure it was water proof, I had a contractor who specialized in this, spray the outside of the stem wall with a tar like compound and then they applied Delta Dimple Mat" over that (see link below). Then a well designed foundation drain to carry away and water that seeped thru the dimple mat. Fortunately for me, being on a slope I could simply let gravity do it's job to move the water. Depending upon your topology, you may need to drain it to a sump basin and use a sump pump to pump it to a good location away from the building.

Sorry for the product recommendation, I try not to do that, but in this case, I think it's justified.

https://www.dorken.com/en/our-products/products/residential/delta-ms.php

Drainage and waterproofing, mostly. If your local contractors are not used to building down, getting the proper attention to details paid to those in construction might be difficult - workers tend to do what they are used to doing, how they are used to doing it; they can often be hard to get to change if you want something they are not used to doing.

Not sure about the termite problem, we don't have them (yet - who knows how long until we do as the climate warms) but even in a fairly dry basement I'd consider a wooden floor to be a risk due to potential moisture issues (vapor, no actual wetness required.) There are nice wood-look ceramic tiles available now that would be less risky. Even if the stucture is "perfectly" waterproofed, if warm, humid air comes into a cool underground level, condensation is likely.

The above response (by Ecnerwal) is excellent in every front. Just want to remind you that, while you can plan everything, you can't plan something which you can't see. For underground construction, the type of underlaying soil, and seasonal ground water elevation/fluctuation add complexities, that can drive up the cost significantly. Thus, it is imperative to contact the engineering service/company that are familiar with local conditions and practices in the planning stage.