A DC-DC converter is needed really, the 1.3Ah capacity of the lithium battery would mostly be wasted
powering the Arduino inefficiently otherwise. 18V -> 5V conversion will reduce the current drain from
the battery by a factor of about 3 compared to using the on-board linear regulator.
Note this in the description of that MOSFET breakout board:
Note: While the MOSFET is rated to 60V 30A, the circuit board traces are only rated to 3.5A.
Find a better logic-level MOSFET (lower on-resistance, perhaps < 10 milliohm), and don't use a PCB
breakout, either solder or use miniature terminal blocks - drill motors pull a LOT of current, perhaps 20A.
The MOSFET may need a heatsink too, although a 10s duty cycle may make that unnecessary.