"Rejected"
If you mean to do this in order to return to the country you were deported from, don't bother. The new passport number is specifically linked to the old and you will be ringing bells each time you go through customs.
Turkey has full diplomatic relations with Israel and has no problem with people having an Israeli visa or entry stamp in their passport.
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.
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.
No, unless you have a U.S. Passport
Passport where exit stamp is posted
Yes. Israel and Qatar have diplomatic relations.
Risky. Ask your travel agent or UAE embassy.
stemp size
It could well be because Norway is not a member of the EU. Though I do remembergoing to the Canary islands a few years back now, before they were in the EU & they didnt stamp my passport
illegal taxation
Definitely! Otherwise you may face difficulties at the passport control gate on your arrival.