I have worked in US for 2 terms in 2 visas from company A.
First term: H1B(petition valid from Oct 2003 to Sep 2006) visa and worked for 19 months from Aug 2004 to Mar 2006.
Second term: L1B Blanket(petition valid from 2007 to Jul 2010) visa and worked for 29 months from Mar 2008 to Jul 2010.

And, right now, I am in H4 visa. I received an offer from company B in US now.
1) Can I use my first H1B petition to transfer it to company B or should I apply for a new H1B petition?
2) When company B is applying H1B, will I be cap exempt?
3) If I am not cap exempt, will I be considered for 2011-2012 quota?
3) Can I start working immediately when I get receipt number for H1B filing from comp B? Will there be legal problems to start working before getting H1 approval as I am in H4 visa?