Assuming you are applying with your **Italian passports**:

1. **Other passports or identity cards:** Answer **Yes** and enter your Israeli passport details, using the **passport number**. The question specifies identity cards issued **for travel**. My reading is that your ordinary Israeli *Teudat Zehut* does not belong in that section. If you report a qualifying travel identity card, use its document number. ESTA also collects a separate **National Identification Number**; that is a distinct field. [CBP’s description of the information collected](https://www.govinfo.gov/content/pkg/FR-2016-02-23/pdf/2016-03867.pdf).

2. **Your father’s employment:** Answer **Yes** and give his **current self-employment details**. Enter **SELF-EMPLOYED** in the employer-name field and provide his business address and contact information. He does **not** need to use the employer from 15 years ago. CBP’s ESTA help explicitly allows self-employment as employment information. [ESTA Online Help, hosted by the U.S. government](https://www.reginfo.gov/public/do/DownloadDocument?objectID=50695601).

One current update: **Israel now also participates in the Visa Waiver Program**, subject to the passport and other eligibility requirements. Whichever passport you use for the ESTA application, use that same passport for travel to the United States. [Official ESTA guidance](https://esta.cbp.dhs.gov/faq?lang=en).