I'm a permanent resident and I would like to know if I could sponsor my daughter who is over 21 and is currently on F1 status. If so, would she be allowed to stay in the U.S. if her visa expires during processing? How long will this process take.
I am assuming you are asking me whether a green card holder can apply for a green card for an over-21 child. The answer is yes, as long she is unmarried, you can. But she cannot stay in USA based only upon the fact that you have applied for her.
Check out the Visa Bulletin: http://www.immigration.com/visa-bulletin