Hey buddy!
Technically you could certainly commute when on EF. But it more than likely would require a few nights per week in a local Bed and Breakfast near the airport and some clever bidding!!!
As for pay, well I wont go into it for obvious reasons here on pprune.
If its longhaul you are after then avoid applying for LGW EF as the wait could be anything up to and beyond 5 years as you must transfer to LHR EF first! Once your on LHR EF the wait is as little as 18months at the moment. Of course you could be lucky like me and get direct entry into LGW WW. But that oppurtunity is rare although a number of courses are starting next month.
Let me know how you get on.
All the best!