green card I485 pending and buying a house in US?

Yes to the first and third question. For the second your adult child(ren) can be co-owners, but I'm not sure about the inheritance tax. If you co-own with your children, the senior property tax exemption will be limited or not available though, depending on the state.

Immigration law does not restrict property ownership in any way. I know people who own houses in the USA as investment property that have never even been here and have no immigration status.

The problem is your lack of credit history may lead to a higher interest rate anyway and balance out any other positive tax incentives that you may gain. Especially with the credit tightening in the current economy, and even more so if your child has a very good credit history, since they may get better terms getting a mortgage themselves (if that is an option).

I think the best thing would be to meet with a reputable bank or mortgage broker and discuss your options.

Anyone can buy a house if you have the money. Even if you are to visit it every so often.

You could buy the house along with your son. I would suggest you buy in joint ownership which means that you both own the dwelling in the same interest, and God forbid something happens to any of you the survivor will own the house in its totality.