I know I know I know get it removed get it removed or the soil tested.

The $200-$300 dumpster rental you'll also need to get rid of the excess soil around your house will be well worth the expense.

The crawl also appears to be quite moist, since there weren't any vapor barriers set up to prevent moisture from building up.I am worried that over time the soil could shift, causing the supports to give way.

Sounds like to treat soil and tent the property would be $1300.00 and the seller would split the difference.  

One approach might be to rehab the property like you otherwise would, which would include repairing the exterior to cover the crawlspace appropriately, and perhaps improve the drainage near and around the foundation to prevent soil erosion/shifting.  

However this won't work because there are protruding ceramic soap dish and tooth brush holders hanging off the wall now, and I think a mirror at full length means it will be sandwiched between the wall and sink, it will most likely crack as I tighten and mount the sink against the wall...Plus it will be a big hassle to cut the holes underneath for the one drain, two supply lines and two sink mounting holes.

I know that there are no utilities in the lot, and I don't have a good feel for the soils/septic/city sewer situation there.

A "town home", as long as it is fee simple (it includes the land/lot underneath it) is the same as any other SFH.

All three signed the same page on the lease which has all three names, their addresses and phone numbers and rent/security deposit etc.The tenants left so much trash and soiled kitchen, I couldn't show the house to prospective students for the next lease term.

Easy fix, grout, maybe put some tile sealer down to help the grout, and enforce the wood underneath.