The captain could allow the enlisted men to have beards, although officers were more likely to have them.
The holster is correct, it was called a "pistol frog" by the Navy and does indeed resemble a sword or bayonet frog more than a holster, and especialy with a cutlass on the left side the right side butt-forward carry is correct, but both types were issued and worn.
Axes were sometimes passed out to the boarding details when combat was imminent and boarding was contemplated, but that was more likely back in the day before revolvers and were quite "old school" by the time of the WotR. Even so, the Navy still had them right up to WW2 - we're such traditionalists
No, the problem is that blue undershirt - Navy undershirts had a square head opening, not the modern rounded t-shirt type opening.