Is Technology Alert List (TAL)/Visa Mantis background check also applicable for green card for an immediate relative (father)?

I think so.

F2 visa rejected on june 8,Can i apply for H4 visa before Oct 1.Which is the right time?wil f2 rejection affect my h4 visa

What was your underlying status?

I am in my OPT grace period in the process of applying for change of status from F1 to J1. Can I carry on working while I wait?

No.

Does having a stokes interview make it easier to obtain an i751 waiver

The prior interview is irrelevant. Now you are worried about the 2 year period after the interview and proving the marriage is real.

F2 visa rejected on june 8th,Can i apply for H4 within 3mnths of F2 rejection that is before Oct 1.What would be the Right time?

Problematic. Se an attorney.

F2 visa rejected on june 8th,Can i apply for H4 within 3mnths of F2 rejection that is before Oct 1.What would be the Right time?

Repeat.

Can I file another I-140 while my husband's I-140 and I-485 is still pending, and we are not having any status now

Yes you can.

It all depends on your situation. I think now is the time to finally hire an attorney.

My case is still pending and I need to change my address.

You have to answer truthfully with an explanation

H1 Visa Stamping after I140 is withdrawn/revoked from the previous employer

Good question. I would not go if it were me and I had no underlying 140. But in reality it should not make a difference.