So, like everything else in the world, Pokemon has a wiki all of it's own. You can find it, Here (it's called Bulbapedia).

To answer your specific question, Paralysis is one of Five Status Conditions that a Pokemon can be effected by (the others being Sleep, Burned, Frozen and Poisoned). If your Pokemon is Paralyzed then it's speed is halved and it is unable to make a move a quarter of the time.

As to the rest of your questions: -Battles can last for almost any amount of time dependent on certain factors, however most battles should take between 3-10 minutes to complete realistically. -LC (Little Cup) is a singles tier, meaning that it's only one Pokemon out at a time on each side. There are certain tiers that are Doubles tiers (two Pokemon out at a time on each side) and even (in the past at least) a Triples tier (You guessed it, three Pokemon out at a time). But we don't really need to worry about those this year at least.

No worries about it. To ask questions is always good. If you need or want anymore help (and if anyone else wants any help with Showdown or Pokemon Battling) you can either message me on Discord if you're on it too, or my email should be clickable (I'm just not always that quick to respond to emails).

Nova