H4 re-entering US after H1's Employer changed while extension from old employer is in progress

[Sumit0907]

I am staying in US with my H4 wife and working for employer A and my H1 is expiring on 06July2017. My employer A has filed extension a month back for me and my wife's I-539 in regular processing. My wife had to travel next week to India due to family urgency and planning to come back on 3rd week of June(2-3 weeks before  expiration). 

 Meanwhile I have got a good offer to join a new Employer B(20 year old US based midsize company) which will be filing my H1 transfer in few days and I will be leaving Employer A in 3 weeks( considering I get H1 transfer receipt within next 3 weeks).

Questions:-

1. Will there be any problem in changing job to new employer while extension under process with old Employer ?

2. After 3 weeks I will be working for Employer B. Can my wife enter US on 3rd week of June with the stamping she has on her passport from Employer A which is expiring on 06July 2017 ?

3.  Should I file my wife's I-539 along with my H1 transfer to new Employer B ?  or should I file my H1 transfer now and wait till my wife comes back and file her I-539 then ?

Or please provide any other suggestion.

Thank you so much.