How much time does it usually take to get RFE post selection of H1 B in lottery?

Hopefully, your employer will not receive an RFE. If an RFE is issued, the waiting period for an approval depends in large part how long it takes...

Will it be of any use to pursue my green card given my circumstances and am I illegal?

If you believe your attorney has provided false information, you should seek a second opinion with a different attorney.

This depends on the applicant's country of birth, since some countries have severe waiting periods for visa availability under the EB-3 category. ...

Regular vs Premium Processing for H1B extension?

These types of questions could only be answered competently by an attorney who possesses all material information involved in the petition.

Asylum

The US should not inform your home country of any application for asylum.

If I was recently charged with pc242 and released on a citation. Can I leave the country for a period of 24 hrs for a funeral?

You must discuss this with a criminal defense attorney.

If my husband have A7 year joint suspension case and his case that he called was ran current cur ? Does he still have to do the

Not sure exactly what you are asking here. Perhaps you could rephrase the question?

An illegal immigrant mom has a kid with a US citizen. Proof of employment.

You should consult with a Family law attorney.

Question regarding H4 EAD renewal with H4 renewal application receipt?

You must be very careful in submitting these applications. CIS is being very tough on even the smallest errors these days.

Can we apply for H4 to F1 Change of Status without submitting spouse H1 visa?

You should be able to apply for the COS to F-1 without your husband's H-1B documentation, however, CIS may very well request proof of maintenance...