Piloting is a very specific skillset that requires an enormous amount of dedication. That's why most people you know don't pilot planes. That's not different for soldiers; the vast majority of soldiers have absolutely no idea how to pilot an aircraft.
Finn hasn't used ship canons before
Based on the fact that he was taken on a ground assault, we can assume he's an infantrymen. Most infantrymen don't actually have any experience firing an aircraft's weapons. The closest they get is being a door-gunner on a transport craft, and even then you're only going to have one person gunning out of an entire squad due to the number of mounted weapons vs. the number of troops in the transport.
There are nothing but soldiers on the Starkiller. That means every job
has to be done by soldiers or droids. Generally, this means that soldiers who fill other roles (usually lower-ranked, newer soldiers) will have "duty" lists that include things like janitorial work, guard duty, etc. That doesn't mean he's some kind of specialized "Sanitation Trooper". That's ridiculous.
Again, this parallels the way real armies work. You generally do not have janitors on a forward operating base. That means someone has to do the menial, unskilled labor jobs. Every soldier you have ever met in real life has mopped a floor at some point, that doesn't mean they are somehow incapable of fighting.
Every non-ranking Stormtrooper stationed on the Starkiller should have
some tasks they are doing when not deployed directly in combat.
When not having a weapon he was desperate for a blaster
Again, that's just normal and sensible. I used to lead Army Combatives exercises for my platoon, I taught other soldiers how to fight hand to hand. The first advice I always gave them was, "Don't, if you can avoid it. You have a rifle for a reason."
Normal people prefer having a gun to a sword, given the option. Jedi are, for obvious reasons, a special exception to this. The fact TR-8R had such a mad-on for personal combat with Finn that he tossed his blaster is far more questionable than the fact Finn would rather have a gun than a sword.
And last, there is no evidence of any other stormtrooper having these riot sticks which make me say that it was pulled out of TR-8R's ass just because it would be cool.
Again, it's a riot control implement. That's why he had the shield along with it; it's directly analogous to a riot control shield. (Which, despite what COD tries to teach people, is not designed for stopping bullets and should not be used as cover wading into a firefight. It's purely for dealing with lightly-armed civilians.)
You bring a couple of them along if you're trying to take captives alive, but unless for some reason the First Order decided to move to doing police operations and no longer wanted to cause any civilian casualties, there wouldn't be any reason to deploy the entire platoon with them.
For an easy analogy, note Flamethrower Trooper in the opening scene. Why is he the only one with a flamethrower? Because having everyone bring a flamethrower would be dumb, even if you're on a search and destroy mission where a flamethrower is actually going to be used. Why didn't anyone bring a flamethrower in the TR-8R scene? Because they were actually looking to take at least some live captives or quell civilian resistance, rather than murdering everyone present.
I forgot to quote the user who said it, but outfitting some more stormtroppers and Finn with the riot stick at the village would have solved the entire issue.
As stated above, that would be nonsensical. You don't bring a riot baton and a flamethrower to the same battle. Those are about as diametrically opposed as two things can get when it comes to tactical equipment.
We are told Finn is a trained solider, the above showing working against that. We are shown Rey beating up some thugs with her staff. Which one would be more believable to handle a light saber?
I don't really have a problem with Rey being able to put up a fight with her lightsaber. I think people are way too hung up on the idea that there's some discrete "tier" that each character is in, going so far as to say, "Well, if Rey beat Kylo, then obviously Kylo's no threat anymore."
I mean, that's just not how combat works. Life or death melee isn't an "any given Sunday" sport, there is literally never a situation where a person is so "OP" that someone waving a knife at them ceases to be a credible threat. I'm kind of surprised that people even have an intuition for the opposite case, but I guess a generation of DBZ and cornball action movies will do that.
I'm not saying you're entirely wrong, by the way. Obviously, if you had these thoughts, you are not going to be alone in that. There may be a significant portion of the audience who had the same thoughts you did, which means that Abrams could have done a better job conveying the message he intended. No question.
I do think the further you dig trying to justify it, the more nonsensical it gets, though. You should just
stick with the surface-level reaction: "To me, that felt like it didn't make sense." The director's more concerned with your gut reaction and intuition than an actually deep, logical cohesion, anyway. The fact that it bothered you on an intuitive level is enough.
(I'm not sure what to do about the portion of the audience that needs complete justification for any character "beating" any other character, though. Tell them to stop playing so many MMORGPs, I guess?)