Then just grading like concrete or something around the back of the house to stop moisture from coming into the basement or affecting the sidewalls. 

The other is they now want a vapor barrier installed in the floor but these are older model trailers “as is” and we haven’t had an issue with mold or moisture.

These items can last for a very, very long time if moisture, humidity, and bugs are kept away.I specialize in pre-1950s houses and have one from the 1910's. 

You will need some space for the second unit, preferably close to the first unit, so that tapping in and re-routing the ductwork is minimal.Alternatively, dedicate the existing HVAC to the larger apartment and install a mini-split system for the other.One of the issues with both solutions is that the existing HVAC will be oversized for just the single unit, which can lead to issues with moisture removal during humid periods, but in my case, this has worked fine for several years now.

That way if the heater rusts out or the pressure relief valve blows, it won't (hopefully) flood the apartment under it.Lastly, install a moisture sensor in that pan that will sound an alarm so everyone knows something is up.

But I'd say if you personally are going to live in the home, I'd definitely lean toward doing it.If you see no indication of moisture issues or anything else that makes you think mold is an issue, then I'd say this is optional.

(for eg: grading of the house outside, rot, exposure to moisture...)I am worried about the long term expenses that come along with it?

Most people think they're OK taking out the little roots and not messing with the big roots, but it's actually usually the opposite - large roots just stabilize the tree, while the small roots are the "feeders" that provide nutrients and moisture.

Steel, tile, slate, etc are all significantly more expensive, and decking issues beneath the existing (due to moisture, etc) will also significantly increase cost.

Also, your "inspector highly suggested getting a termite bond"... is there reason to think there's termite/moisture issues with the property?