Response to your questions:

Yes potentially, DDP keeps loss local to each model and averages gradients, which might produce different result compared to having a global loss and back-propagating from there.
Also potentially yes, batch_size is another hyperparameter that can be tuned.
As a general note it is good to re-tune all hyperparameters when switching to DDP. These hyperparameters can all affect the accuracy of the model when compared to single GPU. However difference in accuracy should not be very drastic (this is subjective), if that is the case then it requires additional investigation.