My mother owed me for a sum of money I lent her several years ago with intent of paying me back when she sold her home. Is that allowed?

Nope, I had a notorized loan agreement which included interest. It was essentially garbage. Medicaid is a supercreditor.

Is this an old and dated IOU that has been documented in every way? Does your Mother's POA see evidence in her papers of her loan to you? If there is documentation of this loan then the POA can see to it that this loan is paid according to the agreement stated in the documentation.
If, however, YOU are the POA this is all more difficult. You can imagine that were someone truly nefarious, they could get POA on someone not able to handle their own affairs, and then make a fake IOU and pay themselves? A POA must never ever be seen as doing anything "self-serving".
I am assuming someone is handling spend down for your Mom? And she is unable to make her own decisions? If she is able to make her own decisions and has documentation of her loan and it's agreement, she can repay you. But, again, Medicaid can call this amount into question. Because, again, Medicaid can claim that your Mom is simply transferring money to you with some made up story. Try to see it from their side.

If you have propper paperwork, you may be able to put a lean on the house. Good question for a lawyer versed in Medicaid.

No. Unless you executed a promissory note and documented it, Medicaid will view as gifting.