While you are the one who made up numbers without any explanation and thus you should be the one who needs to answer this question I will humor you.
Ahem... when talking about AD&D I did give you numbers: the default assumption of a pirate lord being between 8th-10th level, citing the PHB & the MM. Fair's fair and all.
1. You have a very wrong idea about pirates. They were probably the most democratic people during the Age of Piracy as captains were most of the time elected and had laws on their ship, including "social security". But ok, lets assume pirates are just a chaotic evil orc horde on a ship.
Oh, we're talking about
real historical pirates now. I didn't get the memo. Or the goalpost shift. Regardless, I imagine real historical pirates elected captains based on their competencies, which in later D&D is expressed via level. Of which "4th" isn't very high, given most campaign settings I'm familiar. Certainly not high enough for someone labelled a "lord", unless of course the "lord" part is ironic.
We wouldn't happen to be discussing ironical pirates, would we?
2. Assuming that the sailors are all level 1 commoners and experts 1 or 2 levels of fighter is enough to have way more skill than any of them. If they are all level 1 warriors, 2 levels are probably for the best. Of course that is only necessary if you hold them together by force. A unrealistic concept but you seem to expect it for some reason.
OK, so we're talking 3e now, right. Expert & warrior NPC classes. Since level determines not only combat ability, but all other skill competencies via the level-based skill rank cap, a "pirate lord" with 1-2 fighter levels would be hard pressed to consistently make
either skills checks
or the combat rolls to keep their crew in line.
In fact, fighter would be the worst choice of class. At least a rogue would have the breadth of skills required for the job (if not the bonuses to the rolls).
Also, assuming the crew is mostly 1st level commoners & experts would make them less combat-capable than the staff of your average bakery found in a bad neighborhood of Sharn (the big city in the Eberron campaign setting, in case you didn't know). Who did these pirates pirate? Retirement communities?
3. The skill DCs entirely depends on your performance as captain.
The skills DCs depend on the situations the crew get into. What do suppose they might be for a "fighter lord'? Given the way you low-balled the crew levels, I think the issue here is you're using the words "pirate lord", but you mean something closer to "mediocre scrub captain leading a group of even scrubbier pirates", in which case I concede the point!