Travel on H4 - H1 Stamping In India or Come Back To US On H4 To File COS?

I have a situation here, I am currently H1B approved under 2013 quota and currently in US on H4. However I have an emergency and I need to visit India for two weeks. I have few questions related to this

  1.  I am currently on H4 status which is valid till Dec 13, 2013. Is it ok to travel to India at this point in time and return on Nov 24, 2013?
  2.  My employer A who filed my H1 has no projects in hand currently. However if another company B offers me a job, can I go for H1 stamping in India on company B’s appointment letter (I have no pay stubs with employer A as he could not get me any project till now and am still on H4 status as of now)? If it needs H1 transfer how long would the process take? What is the procedure?
  3.  If suppose my H1 is rejected, can I still travel back to US on my H4 in Nov? Or do I just come back on H4 (without going for H1 stamping while in India) and let the other company file for COS eventually?