No, having an Israeli stamp in your passport may prevent you from traveling to Iran.
You can't. At least not on the same passport. You should have asked the Israeli officials to put the stamp on a small slip of paper you would have carried in your passport.
Yes - you can. You would be denied entry if you are an Israeli passport holder. Courtesy - Air Ambulance International vibha.info
Yes but you may be better off not getting the stamp in your passport. You can ask them to stamp a piece of paper instead.
Yes. Israel and Qatar have diplomatic relations.
Risky. Ask your travel agent or UAE embassy.
Of course you can. You can enter just about any non-Arab country with an Israeli stamp. Even amongst Arab countries (the ones who don't accept Israeli passports) there are maybe 5 that won't grant entry because of an Israeli stamp.
Yes, although they may not travel on an Israeli passport, the UAE as most Arab nations does not recogonise the governement state of Israel. The same applies to anyone visiting who may have an Israeli entry or exit stamp in their passport.
No. Oman does not accept Israeli passports.
If it's a valid US passport or you are a dual-citizen most likely
Yes, you can request the immigration officer to stamp your passport.
Yes, did you get a stamp in your passport when you left the US?