A: You can structure the trust in several ways. It depends on exactly what your goals are, if you are looking for asset protection or another goal, tax goals, etc. Would need to speak with you to get some more information to help advise you on the best route to take to achieve your goals.
A: There are many issues involved in this question. I would need to see the original deed and mortgage on your house plus the contract you signed with the contractor. The original mortgage almost certainly had an acceleration clause stating that if you sold the property, then the full mortgage becomes due. Going after the contractor might be possible but other avenues would more likely be the better route to keep your house from being foreclosed. Will also need to see if your contract gives ownership to the contractor or just the right to sell on your behalf. Lots of additional questions that need documents to give you your options.