score:4
I can answer one of the two.
My father is self-employed for more than a decade. Should he fill there his last employer (from 15 years ago)?
to quote the Electronic System for Travel Authorization (ESTA) Online Help:
Employment information can include: self-employed, student, child, homemaker, stay-at-home parent, or any other word to describe employment status.
Answer "self-employed" accordingly.
Note this is sourced from a .gov site. This is extremely important. Any and all ESTA answers which do not come from a .gov site should be treated as false, plain and simple. There are a huge amount of scammer sites around and they will have information sections of very questionable validity.
So let me note you should fill on https://esta.cbp.dhs.gov/ and nowhere else.
Upvote:1
Re the first question:
Have you ever been issued a passport or national identity card for travel by any other country? - I have Israeli passport and I believe I should fill it there. But there is also an option for National Identity Card Number. Should I fill it as well? If so, should I fill the national ID number or the document number?
Israeli national identity card cannot be used for travel, but passport can. European national identity cards can in fact be used for travel (within EU). Since "other" refers to Italy, the Italian identity card that you may have is irrelevant. You should fill your Israeli passport details here (the passport number, not the national id number).
From the same source as the other answer:
Q8. What if I have dual citizenship, but my non-VWP passport is expired or I do not have a passport for that country?
A8. If you have any additional non-VWP passports, please enter the most recent passport information, even if that passport is expired. If you are a dual citizen but do not have a passport from another country, select the country from the drop down list and do not enter anything in the Passport Number field. If you do not enter a passport number, you will still be allowed to continue with the application.