I am blessed to be gainfully employed by a large fortune 500 company and have been approached by a small company in the private sector with a compelling offer that I would like to accept.

I notified my employer of my intent to leave, who asked me to pause while they assemble a counter-offer.

**The Problem**

The small company package is 20% more valuable than my current wage.  The large company plans to counter with a package 30% greater than my current wage.  

**My Questions**

1) After I receive the counter offer, is it courteous/acceptable to approach the smaller company and ask them to match the larger offer?  If so, is it unprofessional to ask both parties for a best-and-final offer?

2) In the event I accept the smaller company's offer, the large company asked that I consider contracting my services for 6-12 months after my departure, nights and weekends.  Is this common? The companies are in different industries and are not competitors.