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I have flown to Tel Aviv several times from Zurich and Hong Kong but always on El Al so I am not sure if the same security screening will occur but here it is none the less. You should check the following with the airline.
On every flight in and out all passengers were subject to an interview by security personal, it pays to know where you are staying, have all of your documents handy and if on business a letter of invitation, and of course be very early as the interview can take anywhere from 20 to 45 minutes or more. Above all keep your cool, I remember on one exit interview a colleague was frustrated and that cost us an extra hour of checks.
Getting a cab from the airport shouldn’t be too much of a problem, I seem to recall the road out is lined with eucalypt trees which is something odd in that part of the world. Downtown will be quite but most tourist cafes etc will be operating and around 9 or 10 PM the streets will come to life like someone flicked a switch. Hope this helps.