The power jack on the Arduino Uno board can have 7 to 12V. About 7.5V is the best.
You could use a DC-DC converter to make 7.5V out of 24V.
You should have a look at DC-DC converters, They are fun to use (in my opinion).
The bluetooth module at Adafruit is working and is compatible with the Arduino.
Cheaper modules from Ebay have to be tested first, and the range might be very disappointed. I think it is easier to start with something that is working.
There are many motor drivers. The size does not really matter, and most "dual" drivers can be uses in parallel mode.
Modern mosfet drivers (or chips with mosfets) have a very low Rds(on) of a few milli-ohm, those can use small boards.
Older drivers without those modern mosfets need to be bigger.