Unless the professional you called is qualified* to say the tree was an immediate hazard and given the situation, it could not wait to be remediated because property and/or life was in jeopardy, you're going to be on the hook for the removal and could also be on the hook for the replacement of the tree + additional damages. 

most work is flooring, remediating the basement, paint and updating one bathroom along with siding repairs/likely window replacement and massive landscaping and  concrete work I like doing.

Depending on the auction terms it could be that result plus the forfeiture of your deposit, or perhaps the trustee/auction company must elect one remedy vs. the other.

I had a water leak at a property that required remediation.

Hopefully you can get remedy quickly. 

Legal remedies can get costly.

It tested low: Highest levels are .3, well below the 1.5 legal limit for contamination.However, it’s been suggested that I still might want to hire a remediation company to do HEPA-vac + wet wipe throughout the home.

I just think if you worried about people stopping paying you and don't have protocols in place to remedy if that happens you should not own rental properties at all, since in theory renters can stop paying you as well, the likelihood of many of them stopping paying you at once?

Check out the sales data on when it was last sold and if it was recent within the last 12-24 months be careful you are not buying something that may be maxed out in current market value.Only way to remedy that solution is to buy and add sqft like extra bed and bath or larger GLA but room counts can be best.

What remedies do I have against the fraternity?