Mother's visitor visa rejected as we have mentioned Alien petition of my father ( who died) in DS 160 form?

[Umangp44]

Situtation:

I am currently in US on H1B visa, and wanted to get my mother here in US on visitor visa.

My Father's sister has filed Petition for alien relative back in 2006, my father died in 2020 due to covid in home country ( India). I-130 is approved in Oct 2022 ( we received i797 Notice of action) in Nov 2022.

questions:

1) Is my mother still eligible to come to US on same petition once priority date will become current of this F4 category of VISA? beneficiary has my father's name only in i797 which got approved in oct2022 and main beneficiary ( my father) died in 2020.

2) My Mother's visitor visa ( B1/B2) rejected today as we have mentioned about this petition in DS160 and interviewer asked my mother if anyone has done petition on your behalf.

My mother replied, petition is on husband's name and he died in 2020, visa was rejected with 214(b)

in above question no 2, was it correct to mention about existing petition which was on my father's name?

If I want to re apply for visitor visa, handle this scenario?

Please advise, Thanks in advance.