Yep, the motor driver is only 10A and rated for 15A peak, please note additional heatsinking and airflow is required for 10amps.
You need to determine the stall current of the motor you're using, this can often be done easily by simply measuring the DC resistance of the motor coils and using the voltage and resistance to figure out it's maximum draw. You also need to consider how much load you'll place it under. 2.5amps is probably it's no load current rating after starting, and it's stall current will be worst case scenario, if you can approximate the percentage of it's full rated load you'll be using this will be an important number as well.
If the stall current is above 15amps, or your average expected load is going to be at or near 10 amps you'll want to consider a new driver.
No the fuse will not prevent shorts from happening in the controller, first of all the 20A fuse is 5amps over it's rated max current, so even once it gets to the point where the fuse will trip the motor driver will likley already be fried.
So determine the stall current and you can proceed from there.