Ah, thanks for the additional info. Batteries are expensive, you don’t need to replace it.
You ask a good question.
The real question is what is the LVC (cutout voltage) of a 48v controller and the 52v controller. They very well could be the same as it is not unusual to use a 48v controller with a 52v battery. But you need to know, otherwise you won't be able to get the duration you expect out of your battery. It’s a critical question.
a) No. That is a pretty minor change.
b) Your bike will be a little faster. Speed increases linearly with voltage, so your speed will increase by 52/48 (8% faster).
P.S. You are welcome.