How much does an immigrant case stay in undergoing administrative processing ?

Depends on the background of the case.

My husband's green card expired last year and now needs a new job.

Better to renew the card (or even apply for citizenship).

Yes, still pending. You can do an infopass every now and then to inquire.

Just an unlucky case of timing. Try calling the 1800 number or do an infopass. If you have contact with your old address, check that out also.

Voluntary Departure (F1 overstay)

Possible through written motion. .

I have H1b visa and my sister is US citizen.. How soon Can i get a green card if my sister file petition for me?

Depends what country you are from. Philippines for example it’s 24 yrs, other countries (not India, China, Mexico) about 10 to 12.

Should I re-apply for a green card, even though I was previously rejected 2 years ago for false claim of citizenship?

They’ll deny it again based on the false claim. You should resolve that first if it’s resolvable at all.

What would happen if I applied for citizenship based on marriage and separated after would it affect my case?

If you’re applying w/ the 3 yr rule and you separate while it’s pending and they find out, they’ll deny it and make you wait 2 more years.

How long It takes for an asylee after getting the permanent residence, to become a citizen?

4 yrs 9 mo. from permanent residency.

I'm a housewife my uncle sponsored my husband do I have to sponser him too even tho I' don't have any income?

If you’re the petitioner, even if you don’t have income, you have to submit form I-864 together with his adjustment of status application.