H1B to L2 Change of Status + EAD

[atrangi4u]

Hi,

My wife is on an L1A and I am planning to file for a change of status from H1B to L2. 

1) Can I submit my I539 (COS) & I765 (EAD) concurrently? Are they both adjudicated in parallel? Generally how long does this take?

2) I plan to quit my current job after filing I539. Can I remain in the US while my COS is pending? My I94 (H1B) date is in mid-april 2018, what happens if my COS to L2 isn't approved by then? (It seems that VSC is taking 9-11 months to adjudicate I539s)

3) What are the pros / cons for COS to L2 vs flying out to India and getting an L2 stamped? 

Thanks,

Tarang