H4 to H1B approved;H1B transfer Do I need Paystubs

Hi, Need Help. I’m on H4 so far and an employer A applied for my H1 for 2013 and got approved. The H1 is valid from Oct 1 2013. Currently, I’m attending interviews and am sensing that my employer (A) doesn’t seem to have any clients or projects. I attended an interview with a direct client (Employer B) and got an offer. Following are my questions

  1. Are there any issues with the H1 transfer from Employer A to the Employer B?

  2. I’m still on H4 on my passport, and I plan to travel to India during Feb next year (2014). As I would need to have my Visa status changed from H4 to H1 before re-enter. will there be any issues?

Thank you for your response in advance.