Can I quitclaim my property to someone else in order to avoid a possible creditor?

First you need to understand that your social security and any retirement income is protected by federal law and cannot be taken from you.  The hospital would have to file a lawsuit and obtain a judgment to obtain a  judgment lien.  Every state has a homestead exemption that protects a certain amount of equity in a home.  However even if there is equity over the homestead a  consumer judgment creditor would never take steps to foreclose on a lien.  Your home is not at risk.  Depending on the equity bankruptcy could be an option.  However even that is likely not necessary.  There are a number of other facts that would need to be asked and answered to give you a more accurate answer of what woudl be best.  A quitclaim deed is not the answer. In the end you should be fine.

1) You will still be responsible for the mortgage even if you quitclaim the property. The mortgage is essentially a contract between you and the lender; you cannot escape your responsibility under it by quitclaiming it--you can only get out from under the mortgage if a) it is paid or b) the lender agrees to let you out of it (the agreement or consent of *all* parties to a contract is necessary to modify it, including by letting one party out of his/her obligationsO...which is *not* likely to happen.
2) No, if you quitlaim or otherwise transfer the property in what, under the circumstances, is a  clear bid to avoid a debt or liability, the transfer can be set aside as a "fraudulent transfer" and those you owe money to can still have recourse against it.
If it was this easy to avoid debts and obligations, everyone would do it.