In the series, Captain Scott mentions that the standard EDF Eagle (and possibly the Super Eagle?) uses the same Electrically Accelerated Propellant Drive (EAPD) as the Aurora and Celestia. But, does that mean an Eagle has the same maximum speed as the two Explorer-class starships or could the smaller fighter possibly reach an even higher speed? Or would an Eagle's maximum speed be limited by it's small size and the constraint that would place on the amount of available propellant it could carry?
Its not a matter of faster, but greater acceleration. In the end, yes an Eagle (or any small fighter) could go faster than an explorer class ship, but they would burn up too much propellant and would not be able to return. (It takes a lot more deltaV to turn around at higher speeds.)
The Aurora's top speeds were only meant to be used for going to FTL, as the higher your subluminal at the moment your FTL fields are activated, the higher your superluminal speed. (As an example, say, 0.5c will give you 5c, and 0.75c will give you 7.5c.) Of course, the Jung FTL fields are much better, so they don't need anywhere near as much speed to achieve FTL speeds of 10-20c.
For the most part, all ships in combat are traveling at considerably less speeds than what you would use to achieve FTL. Otherwise, the combatants would pass each other so fast, it would be near impossible for them to get more than one shot off.
One shot that could easily miss by the diameter of a planet.