Alot of stuff can actually cause stun damage, you can look at weapons in ufo pedia which generates stun.
Hitting someone with a sledge hammer can stun, but you are also most likely smashing his brain out of its skull.
Batton does exist but for some reason XCOM doesnt start with it. But electric baton seems to be a better way to subdue something like a giant spider than trying to mash it with a stick, because if its alive, then electricity will do something to it.
Not sure about the vest but the standard one should increase the capacity
Tracking works by showing nearest entities that have recently moved, you should use it at the start of the round. However this and motion scanners are things i have never used in any useful way.
Gym works this way. If you go to your agents list (from base menu) there will be a sorting option but if you bring it up you will see more than that. You will see possible trainings or upgrades there and you can assign or upgrade your dudes. Gym can hold up to 10 agents at once which will train anytime they are at the base.
Training permamently increases their stats to a certain level.Eventually, more features will be added. For example Bioupgrades or Tactical implant instalation. These are permament stat upgrades for a fee, you will unlock these as you progress and there is alot of this so by the end of the game, your troops will be abnormally strong, fast and durable. Though these upgrades usually have requirements (In short, your agents need to be able to survive it so they need some training beforehand)
How you use Gym in practise is to slap 10 dudes there all the time (Or 20 if you make 2 gyms) while you use the guys not assigned in gym to train them in missions. So when you reach the point where you can field more than 6 guys, you will have reserves of atleast average troops. Not sure about exact numbers and timers of improvement so i wont comment about it.
About chemwar suits.... yes you cannot know what you are against so unless you want to abort the mission everytime you fail then i would suggest ignoring this type of armour and just rolling for the most universally strong armours you have. Froggies have short range and their attacks are rarely lethal and your guys can wake up on their own so its possible to do their missions but you need to have long range capabilities or better yet just evac and fight somewhere else. Once you will get Tanks they will make this enemy absolutely irrelevant because tanks have too high armour to be damaged by their attack. Hazmat suits have a sidegrade variation called Bio-Exo suit which has alot of protections geared towards creatures in particular so it gives protection against creature-source damage like slashing so they become more versatile but i still prefer Coveralls against creatures due to mobility bonuses and here is another important thing, Creatures will one or two shot your dudes anyway (if they hit), unless you start running around in something like a powerarmour, then the best defence against creatures is to maintain distance (or flight once you can) While this exobio suit will protect you from rats and beetles it wont protect you against things like werewolves who have enough damage to even damage a tank and will most likely one hit KO your guys from full health.
So the chemsuit is only useful if you know you will face long range chem-based enemies and there is a mission type where its most likely useful called "Exobiological Contamination" if you see this mission, get everyone in chemsuits for this one and pray for the best.
I am not sure about research time but yes, you need to put someone on it to give you an estimate time of finishing. And yes the more people you assign the faster it will finish.
2H weapons are usually well things you would use with two hands IRL, rifles, rocket launchers, sledgehammers but if you are not sure then you can check it out in the UFO-Pedia which will tell you if the weapon has 2H penalty.
Nope, duel wielding is possible with ranged and melee as long as the weapon doesnt have a penalty (ufopedia)
Aimed mode tends to ignore or be more tolerant towards the distance falloff, in UFO pedia you can see the maximum range before the average shot will start falling off in accuracy
One thing i actually learned is to remember misisons by their music, because missions have only 1 track assigned for it you can easily memorize them and know what you are up against.
Day or Night will show up before you launch the mission, if its night (if your craft arrives and its night on the geoscape) then there will be a moon in the mission launch screen before you get to your gear.
Yes, Backpacks are tied to armours, most stronger armours have it but flying armour doesnt due to the space being occupied by a jetpack.