I doubt the Slalom version was different under the hood. There were a couple of other 'specials', like the "Wolfsburg Edition" Jetta's - but I think its differences were the outside and inside trim and maybe fancier wheels. My Jettas both had a fold down center section to the rear seat. It has armrests for the passengers, and coupholders in the middle. On one of them the prior owner had to knock that center piece out - due to having locked her keys in the car, but having left the trunk unlocked.
Anyway, the items in your pictures: The 4 injectors are all alike, and lined up. If you see the 4 spark plugs; they are in the front of the engine head. The 4 injectors are opposite them, in the back of the head. They arent easy to see because the round Idle Air Control valve is in the way.
In your first picture: "the round contraption with the white hose/wire" is a vacuum operated diaphram. When the engine is running the vacuum pulls the diaphragm inside, to open the charcoal cannister so the engine can slowly suck in the fuel vapors. Its part of the 'evaporative emissions' control system.
In the second picture: "the hoses on the side of the big flat box" are vacuum lines. One brings vacuum from the intake manifold. Inside the box (the air filter housing) is a thermal valve, whose job is to let the other hose see a vacuum when the air coming into the air filter housing is cold. The other hose runs to a vacuum diaphragm under the air filter, that opens a plastic flap to suck air in from some sheet metal wrapped around the exhaust manifold. This brings in warm air, since the engine runs better and cleaner - if the incoming air is warm. If that system isnt working - it doesnt matter much, though the engine may stumble in damp weather that is slightly above freezing.
In the 3rd and 4th pictures the engine looks fine.
In the 5th/6th pictures: that plastic cover that is hiding the top of the gas pedal is not on mine. Either someone removed it and didnt put it back, or maybe the Slalom model had it, to keep snow from someon's ski boots from getting jammed in around the gas pedal?
In picture #7/#8. Contraption 1. That little goody is the 'rear brake proportioning valve'. Its job it to limit the amount of brake fluid pressure to the rear wheels - to help avoid skidding on snowy or slick roads. But if there is a lot of weight in the trunk or back seat - then it allows more brake fluid pressure to the rear wheels to help with stopping. You brake system is a dual type. I think one half of it operates the front left and right rear brakes, the other half operates the front right and rear left brakes. This is for safety - in case of the system springs a leak, you will still be able to stop. It will be a little scary though, as the brake pedal will travel further toward the floor.
In picture #9/#10: Contraption 2. That is the main fuel pump and the fuel filter. The pump is sticking out of the side of that plastic housing. I believe the plastic housing contains fuel, as the fuel pump is cooled by being immersed in gasoline. On mine (and probably on yours) there is another fuel pump located inside the fuel tank. You access that tank by pulling back the carpet in the trunk, undoing the round lid. Then you can see the plastic ring that keeps the fuel pump and fuel level sending unit in the tank. Hopefully you will never need to replace the pumps. They tend to be expensive, and replacement always involves doing more work than you plan on: due to rusty fittings, etc.
When you go looking for parts, if anyone asks if your Jetta is a Mark-1, Mk-II or Mk-III, it is a Mk-II. And Digifant II only refers to the fuel injection and emissions control system. The engine is a 1.8L 8 valve, non-turbo.