Is there a business model where people could pay to sell their timeshares to a shell company and then having the company go insolvent?
You can also do this if it's legal, but the court might not be favourable to you.
Yes. They will sue you in court. Then, when you don't answer and/or attempt to represent yourself, you will end up paying the default judgement. A judge isn't going to nullify a contract on their own. You have to explain to them why the contract is illegal, which is not as easy as everyone seems to think. That is what lawyers are paid to do.