When the steering would not turn – I would guess that this was due to the loss of power steering.
This effect is often observed when the engine stalls for some reason but the vehicle is still in motion – making it difficult to turn the steering.
It may well be that the two issues are related – as Ratter15 says, if the engine runs OK except under heavy acceleration, it is likely that the engine timing is slightly advanced (spark plug firing too soon).
If that is the reason, it should not be an expensive fix (to corrrect the timing).