the client is the only place to find up to date information about every item. Use the item set builder and just read what each item says it does. same thing with masteries. If you want to know what champs do then you can take them to the practice tool and play around with them.
match ups are... well they're too dynamic for anyone to say "this character beats this character" without getting massively flamed for their opinion.
the obvious things you need to know is that range matters.
Sure caitlyn has an auto attack that grants her 650 range, but tristana has a passive that grants her 700+ during late game. Ezreal has a bunch of abilities that grant him 1k+ range and he can spam them intensely, but his auto attack range is less than 600. lucian has 525 i think on his auto, but he can cover a large distance when using his dash. so if he can dash in, auto attack, and dash out he might not take damage.
all this to say that marksmen champions have a lot of damage, but they're easily killed because of their primary design being built on the concept of "this character wants to avoid direct combat and attack from a distance". This makes their gameplay that of how much damage can i do before I put myself in range? hence why you build items that give attack speed, critical, movement and extended range.
next you have to consider attack speed.
if you have a character that attacks 2 times per second and another character that attacks 1 time per second on the same distance then you think about who is putting out more damage. A character that is attacking with 35 damage per half second against an opponent that is attacking 70 damage per attack at 1 attacks per second for example. The fact that a champion has to attack twice is only an advantage when that character has the option of critically striking or running away.
last point is movement.
if you can get in on your opponent hit them and then run out of their range then you can deal a great amount of damage to that opponent without worrying about getting caught out. as well as having an opportunity to outrun their reactions when you go to last hit minions.
beyond all of this there's also the point that you have a secondary laner in lane with you. this laner is going to affect your matchup regardless how well you think you know the game. it's basically a random chance multiplier of 4 on any interaction.
you're also the gatekeeper for drake. when you die/lose turret the chances of the enemy team getting drake climbs drastically.
bottom lane has the most income scaling throughout the game so you're expected to aid in leashing the jungler's first buff. mid is responsible for discouraging invasions. do what you can, but don't die pointlessly. if they bring top to your buff that means the enemy at top is going to be coming back to a losing lane.
that's pretty much it.
your questions about item specifics need to be a bit more... specific for me to give you much more advice.
