Requesting US/UK Asylum,Am i Eligible?

Very unlikely that you will be granted asylum. First, asylum is for people fleeing persecution from their own government, Fear of an attack by Arabs in your own country or a neighboring country is not grounds for asylum. If a war did break out, you could flee to a refugee camp and ask the UN to resettle you in another country, but you can do that only in the event of a war and you cannot pick the country you want to move to. Also, the US is unlikely to embarrass its close ally by granting asylum to any of its citizens. If you want to leave Israel, you'll need to come up with a better plan.