You would want to use your parents address as your semi-permanent residence and apply based on that information.

United Healthcare, Anthem, Assurant and a few others all offer policies for up to six months.

One thing to consider: If you were in an accident and it kept you in the US for longer than six months - your coverage would end and you quite possibly could be uninsurable at that point.

Maybe consider buying a permanent policy and cancelling it after your time here is up.

You can just buy a temporary health insurance policy based your parents’ address assuming that’s the residence you use. I have some links on my site.

You are asking about car insurance for a rental car? If you are then just purchase the rental car’s auto insurance.

Or, you might call your parents auto insurance company and see if you can be listed as a driver under their car insurance.