Are spouses in the i-130 process getting their visas approved quicker currently ?

You could certainly try to get a K-3 visa for your spouse, but their are likely delays in processing such requests.

Getting an F-1 visa after cancelled K-1 and a history of F-1 visa?

Pursuing a K-1 visa may make it harder for you to convince the consular officer that you don’t have immigrant intent. Make sure to have evidence of...

Can I reapply for EAD once I-765 denied?

Yes, you can reapply once you can show you are eligible.

Can I file I-130 for spouse green card if I am US citizen but through asylum case and been citizen since 7 years?

There could be issue depending upon what grounds you sought asylum on.

Can I go on a loop cruise while my asylum status is pending ?

I would discourage you from going on such a cruise.

Can I use my Employment authorization card for travel?

You can find a list of acceptable identification for domestic travel at https://www.tsa.gov/travel/security-screening/identification.

You do not need to invite your parents. Your parents simply complete a DS-160 to apply for a visitor’s visa. They will need to convince the...

No. USCIS may still waive the interview for the Form I-751.

It is not a good idea. The child could end up detained. The parents should consider request humanitarian parole for the child.

How long is RFE processing time for consulate returned case?

You could possibly pursue a mandamus a toon against USCIS. This is a federal court action to require USCIS to make a decision.