Yes, effectively by refusing to cooperate at the I-485 stage.

Hi. I'm preparing Form I-485 for my dependent under the NIW category. On page 4, item 9.a, Do I need to answer yes or No?

The answer to this question is definitely "no."

F-1 reinstatement?

If the reinstatement is successful and your F-1 has not expired you should be able to return to the US.

Will my J-1 get cancelled if I apply for marriage based green card?

You are able to continue your J-1 training program.

You list the same SSN number that was issued to you while on J-1 status.

Can we switch the I 130 application to sponsor a sibling to a different service center ?

No. One does not get to choose which CIS Service Center to have his/her case be processed at.

Does an overstayed father of a US citizen need to apply for adjustment of status based on Act INA section 245i?

No. INA section 245I is for those who entered the USA illegally and have an exception apply to them.

Consider filing a mandamus action in federal court.

Consider filing a mandamus action in federal court

Could have negative effect on GC application - not on the "citizenship", however.