Yes, both clocks are synchronised for both reference systems according to the standard synchronisation convention.
No, that is wrong: according to the standard synchronisation convention, the clocks are now out of synch with respect to O.
- Both moving clocks are now very slightly behind according to R.
- According to O, clock B in the front is now ahead on clock A in the rear.
This is quickly understood with a simplified analysis from the platform: neglecting the small effect from length contraction, both clocks are about equally behind. If O sends a signal to both A and B, clock A is moving towards the signal while B is running away from it. Thus the signals will reach A before B. Consequently, A will indicate less time than B at these events which O defines as simultaneous.