Can you please suggest a best way for her to travel to US?

She will not be able to travel to the USA. She needs a SB1 visa for that.

What is the best way to continue to be in H4 status after Oct 1?

Not to be in the USA on October 1, 2016 and then reenter on H4. Inform the employer to withdraw the I-129 so that the H1B would not be approved.

Will the officer ask about my kids father on green card interview?

They could if this information becomes relevant to the inquiry about the bona fide nature of the marriage.

Both law and the regulations require USCIS to take steps to insure confidentiality of the VAWA application including from the abuser spouse.

Do I need a new LCA

Most likely, the employer would have to amend the I129H not just file the new LCA.

Can I report him to someone for this? If so how.

This is not really a question of US immigration law if you think about it.

Does my travel or visa stamping process have any impact if I am traveling alone. And if my wife can legally stay in the US?

In general, the derivative status is good for as long as the primary status is good. When you leave the USA, you are not in status since you are...

H4 EAD with I-140

you can seek H4 visa at the consulate as you day and when you come on it file I765 for EAD.

How do I withdraw work authorization under TPS and apply for new one under OPT ?

I suggest you talk to the school's DSO about this issue.

Could I change the job using AC21 because my I-485 will be pending more than 180 days but my wife's I-485 is pending for 90 days

If your I485 related to the I140 has been pending for over 180 days and the new position is genuine and of the same or similar nature, you could...