Fear your lost in the noise and labels. You can use most any combination with in reason. Do need to match the Battery and controller voltage.
Motors you can feed until you melt them, the label on it does not make any difference. Motors are rated in Watts not Volts. 52V and 1500w motor is 28a so a 40A BMS should be fine. 48V and 2000w motor is 42a so 50A BMS seems good. Most motors can be ran at 50% higher than rating for short periods.
Batteries you need more information if you over use it or stress it then a short life it is. Need to find "maximum continuous discharge" what it can do with out hurting it. BMS should be rated for more than you will expect to need. Battery AH is an estimate of total energy a battery has, limited to how fast it is discharged.
The controller should fit the speed and power you expect to get out of your setup. less than BMS
The problem is we upgrade the weakest part then another part is then the weakest.