Took Omar into the first quest, had some fun with him, then decided to swap in a better pistol for the one he has. Just one problem. He doesn't have the pistol skill! What the heck's with that. So I couldn't give him the new pistol, and I couldn't put the old one back in, I had to instead give him a shotgun which has abysmal range. Is this some sort of bug? Doesn't make a lick of sense to me. Guy seems to instead have shotgun and assault rifle skills.

I've never seen Omar with a pistol to begin with. Always equipped with a shotgun by default and able to use shotguns and assault rifles. Maybe you were playing a much older version of the game, and recently updated?

Yeah I bought the game when it first came out and installed it because i liked the dev's previous game, but it might've been updated by GOG galaxy at some point. Like I think he's got a skill where he shoots two different people (DOUBLE SHOT) if I'm not mistaken, so a bit weird to have the shotgun for that. Here's a screen grab of omar in action.

Yes, very strange. Here's Omar's skill tree in my game, as it has been for as long as I remember. Note the complete absence of pistol skills, including double shot. Pistols are a girly weapon. Er, I mean, Natalya, Rose, and Annabelle are the main handgun people, right? And Le Fantome, I guess.

When I played again he had the shotgun skills instead, some conical blast. So whatever the bug is, seems to have resolved itself. I haven't played enough of the game to know who would have what sort of weapon- for a pistol, I would think officer or gentleman soldier myself. Though maybe a lot of women characters have them.

I think I possibly unlocked a female character today when I found some nazi raygun. But then I failed the first mission again so, not sure if it stayed unlocked.