1. wire fund over to your account. on tax purpose, it is their gift money to you. No tax issue if they do not have green card/US citizenship. If they have green card or US citizenship they may be liable for gift tax.
2. possibly, but not likely. If the house worth less than 1M, there is probably no inheritance tax issue. But a trouble to deal with ownership change later.
3. put yourself as owner is the best. You will pay tax for rental income.