It usually takes several days to more than a week. Need to wait ans see what the reason for the RFE. It may be any number of different reasons....

US citizen currently married J1 (expired) and she's pregnant (with our plan). what to do to get her greencard?

If the J is not subject to the two year home requirement the J may adjust based on visa petition. If subject to the two year home residency...

When can I apply? What is the next step? Do you have any recommendations?

You must complete the process before the end of the fiscal year. Working with an immigration attorney will be the best way to proceed.

Can I delay my joining on H-1B, 10 days after the start date/valid from date on i-797A?

You must maintain lawful status until you join your employer. 10 days is okay.

My appeal for removal proceeding was approved by the BIA now the prosecutor is appealing at a federal court. What can I do? :(

You will need to respond in Federal court. You should have an attorney represent you.

I hold an I-797 A, Notice of Action, Case Type I 539, Class F1. I'm I eligible for medicaid or emergency medicaid?

Emergency services possibly Medicaid no.

Bridge gap between L1 I-94 expiry & H1 start date?

If you file for an extension of the L1b and it is approved through October 1 you may file for a change from L to H1b It is possible but maybe...

Yes it is possible to change from the 2F. Work closely with your designated school official as you must have the change approved before attending...

For 3 year citizenship rule, one of the requirement is to be married to a US citizen and living with same US citizen for 3 years

You make out three years from the date your spouse became a United States citizen.

Do I have to wait the for the "30-60" day immigration law rule to apply for my wife? We were married outside US and she has B2.

Yes it may apply. Before filing it would be wise to have a consultation with Immigration Jhaveri and perhaps have Immigration turn the parent file...