If I mount a Sparkfun power driver (DEV-10618) on an Arduino Mega 2560, how many pins will still be available on the Mega for other uses?
According to the schematic, the shield uses 6 pins on the Arduino for PWM control (pins 3, 5, 6, 9, 10, 11) - so you would lose those same six pins on the Mega (which are also PWM pins on it - but it also has others if you need them; on the Uno, those six pins are the only six that have hardware PWM).
Given that the standard Mega has a total of 54 digital pins - minus those six leaves you with 48 other digital pins (plus 16 analog input pins). Finally - note that the standard Mega doesn't bring every pin out to a header; there are unused pins that are mapped (that is, you can use Arduino functions with them) - but there isn't any place to connect to them (short of directly soldering to them). That said - there are Mega clones (I think Seeedstudio has such a clone?) that do bring them out to headers.