I've helped place roughly 10 claimants internally and brokered a few others.

Vivek,If you go the LLC route, definitely speak to an Attorney about the do's & don'ts on how to set it up and how to keep it at arms length from your personal accounts to keep a claimant from piercing the corporate veil.  

Would a right of redemption claimant have to reimburse the new owner for improvements as well as pay back taxes to redeem the property?

Science cannot disprove negatives, but it is incumbent upon the claimant to provide proof of a positive, not the other way around.

I'll give my $0.02.In a lenders policy (which is I believe what we are discussing here), unpaid real estate taxes would be covered.However, this claim would probably be excluded under the exception for losses created, assumed or agreed to by the insured claimant -- because OP is refusing to pay a bill he is responsible for.

I never refuse to give someone an application, most of the ones I would like to refuse don't return it anyway.The truth is, the claimant doesn’t actually have to have a case.

Med Pay is when you ask the insurance company to pay a claimant for something you feel you are at fault with. 

If the suit has been reduced to damages and those damages are not paid, there is a potential that the claimant might attempt to attach a lien on the dog owner's property to compensate for the non-payment.

The “mediation” opened with the claimant’s financial demands of $65,000.  

It will only help you if you: 1) are sued for something, 2) you lose in court, 3) the claimant is awarded damages greater than you can afford without selling the house, and 4) you refuse to make a deal with the claimant outside of court.