flap speeds close to min managed speed (f, s, green dot)
......is not the name of these speeds. These speeds are called MINIMUM FLAP/SLAT RETRACTION SPEEDS. That is their name, nothing else. (DSC 31-40-AIRSPEED).
As for turning below F or S speed, we regularly do it, and select below for an improved early climb. Places like BCN with their sharp left turn from RWY 25L at 450 AGL.
In the company I fly for (easyJet) we are not allowed to select below these speeds on approach. I know in BA from mates there that they do on approach.
As for limitations to this :
Obstacle clearance, noise abatement, or departure procedures may require an immediate turn after take-off. Provided FD commands are followed accurately, the flaps and slats may be retracted using the normal procedure as FD orders provide bank angle limits with respect to speed and configuration.