Specials and built-in hull bonuses do not affect drones (such as the combat speed increase of the Strike System or Engine Upgrade or the turn speed bonus of the Ion Thrusters) although tactical module auras do affect drones.
A Navigation Array increases drone turn speed in combat and an enemy Engine Disruptor affects drone combat and turn speed. Microwave Dampener reduces damage dealt by drones and Armor Bypass reduces drone damage resistance like it would any other vessel.
Some drone modules come equipped with built-in defenses to specific damage types but the bonuses of the modules themselves apply only to the module's host ship, not the drones.