L1 EAD 180 days
since u are in your post 180 days, u r in AOS, that means that u can lawfully stay in the US, u can do your Phd, do whatever , except get convicted
as far as your GC goes, it shd be out anyday, my colleageu on a L1 got it in 9 months from the RD of 485
only pray that you don't get an RFE for yr GC and if that RFE asks for the most recent paystubb, u may have some problems, but generally it it is safe and smooth
now, u can do your Phd, u don't need a student visa, coz u r in AOS, but if u travel outside and return back, make sure it is on your AP, not on yr previous employers L visa