That skimmer is a little big for your size tank but it should work just fine, just be careful not to over skim and monitor your nutrient levels.
All skimmers operate in the same basic way to achieve the same outcome, they just have different designs in order to achieve it. All a gate valve does is allow more or less water to flow out of the skimmer body. Think of it like a dam, when it gets too full for your liking, open up the dam to let some of the water out and vice versa. The gate valve on the K2-200 skimmer is just a different style; you turn the knob one way to allow more water out, turn it the other way to keep more water inside the skimmer body. The more water kept in the skimmer body the higher the bubble/water level will be inside the skimmer body.
The silencer helps regulate the amount of air going into the skimmer pump, the air injected into the pump is what creates the bubbles you see. The more air going into the pump, the more bubbles you will have. The less air injected, the less bubbles you will have. Not all silencers have a regulator on them, yours does, you can use it to make micro adjustments to the amount of bubbles in your skimmer by sliding the cover (the flat piece) over the silencer hole or, uncovering the hole completely. Again, they all work the same, just different designs to achieve the same outcome. I suggest playing around with your skimmer to figure out how each part operates, and to figure out how you would like yours to be dialed in.
I hope this helps... please let me know if you have any further questions.