No. Having a pending I-589 does not confer any lawful immigration status on you.

No, you were not an LPR those last 3 years. USCIS does not give immigration benefits unless they are applied for.

You father will get an Alien Registration Number assigned to him when USCIS receives his I-485.

Loosing the physical card is not a problem. File I-751 to remove the 2-year condition.

https://www.avvo.com/legal-guides/ugc/section-245-adjustment-of-status-for-an-about-of-status-with-a-timely-filed-asylum-application

https://www.avvo.com/legal-guides/ugc/section-245-adjustment-of-status-for-an-about-of-status-with-a-timely-filed-asylum-application

Asylum is a one way road, there is no going back to the old country.

It is the date of approval of the formI-485 minus one year.

It is normal for Immigration Judges to take long ( months) to render a decision in an asylum case.

No. This is frivolous filing. Frivolous asylum application renders applicant ineligible for any immigration benefits.