Do Israeli security agents interview all those flying to Israel or is it restricted to El Al flights?

For incoming flights to Israel it is only on Israeli airlines:

El Al, Arkia, Israir, Up and Sun d'Or.

From my experience it also includes flights operated by foreign airlines that are chartered by Israeli airlines.

For outgoing flights from Israel (and internal flights), all passengers go through the security screening regardless of airline.

The real answer is that those measures are time / location dependent.

For non-Israeli carriers bound to Israel - Some locations have this interview procedure ALL THE TIME, some on special periods, and some very rarely.

The reason can be a certain alert ( specific or general ), a political situation, holidays - religious or not , a sensitive time or a sensitive person on your flight,or actually anything else related.

That being said - the interview is usually very short and calm, and what the interviewer is measuring is actually how you react to the interview and questions themselves. So if you just keep calm and answer nicely it can be a lot less "pain in the butt" ..

I myself found that the interviews for other countries ( the U.S. for example ) is a bit more aggressive and invading - but maybe I just had bad luck with interviewers :-) .

I've flown to Israeli from Schiphol and from Sabiha Gokcen with non-Israeli airlines. I've often been interviewed briefly at the gate, though - to my knowledge - not by Israelis. The airlines have: Transavia (= KLM's low-cost), Pegasus, EasyJet.