What to do?

Your mother may travel with valid resident status and a valid passport.

Once accepted at USCIS there is next to zero change of having a refund issued. You can send a letter, however, with a file number it likely will...

It is difficult to be approved for a B visa. Having had a status/visa cancelled in past makes it more difficult.

What is the chances of getting a B2 visa if my J1 visa got terminated and SEVIS got canceled?

There is little chance of being granted a visitor B visa

How much maximum time the F2 Visa holder can take once the visa is approved and entering the US for the first time?

She may travel during the time the visa is valid and you maintain F1 status

Will the effective date be in the past or future when I fill form I539 for a change of status?

The change of status date is normally a date you request the is in or after the date of filing. There is an exception for late filing.

Can US born child with Indian passport get any type of US visa if he need to reenter?

Your son is a US citizen by virtue of birth and retains that citizenship unless renounced.

When to apply for AOS

The earlier you marry and apply the sooner you will obtain status.

I 94 seems error

Contact CBP and they will advise you or contact an immigration attorney to have the matter rectified.

How to respond to one RFE for self-filed I-485 on approved EB-1A I-140?

Recommend that you seek legal assistance with your matter. Contact should be made directly.