is the behaviour of the sim 737 with the limit surge stall realistic?
Don't know, never experienced it in real life
what are the best ways to recover?
Do the recall items, disconnect A/T and reduce thrust until surge/stall stops or until T/L is closed. Then do the non-normal checklist.
theres thrust on the stalling engine right? so no rudder action or?
On CAEs 737NG simulators there are 2 different stalls/surges, recoverable and unrecoverable. Either way initially the engine will produce thrust while it's recovering from the surge, then it'll lose thrust again, recover etc. If it happens during takeoff there will be a great thrust assymetry and you will need to use rudder but you will have to ease out on the rudder when the engine recovers. There will be alot of rudder action until the engine recovers or the thrust is reduced to idle or engine is shut down.
If recall items are not done the engine will continue to surge and EGT will go above limits.