I am currently on F1 -OPT status. My OPT expired on Dec 19th, 2005. I have filed for H4 change of sttaus in October 13th, 2005.
I have not yet received my H4 change of status to date.

I got a job offer now and would like to apply for H1 under premium processing.
My questions are as below
1. Would it be OK to file for a H1 when the H4 application is pending. I am not sure if I can file during my 2 month OPT grace period.My employment offer is cap exempt

2. If my H1B gets approved then what would happen to my H4 application, would they adjudicate if before approving my H1B application.

THe fact that you are in your 60 day grace period is besides the point. The company cannot file an H-1B petition on your behalf until the H-4 has been adjudicated. Unfortunately the H-4 application cannot be converted to premium processing.

If the company does file the H-1B and it is approved before the H-4 (which is likely) than your status would change again when the H-4 is approved, at which time you would no longer be authorized to continue your employment until another H-1B was filed on your behalf.