H1 B approved, COS from F1 to H1B denied. F-1 Visa and I-94 valid till Sep 2016. Next steps?

My H1-B was picked in lottery and got approved, but COS from F-1 to H1-B denied stating that I am not attending school full time. My company opened an MTR with new evidences. I have the following questions:

  1. Can I continue to stay in US and attend school as I have a valid I-94 and F-1 visa?

  2. If I travel outside US for 2 weeks and come back in F-1 status before Aug 15, would I be losing the MTR?

  3. Would I be able to transfer H1-B to another employer while MTR is in progress, since my H1-B was approved?

  4. Do I need to inform new employer about all the above, or a regular transfer would suffice?