I accidentally deleted my draft for this one, so my answers will be brief as I've been typing for like 2 hours.
How can I figure out what kind of damage (ap/ad) the enemy team will be dealing? Press tab and look at the items they are buying.
Is the recommended tab generally the best for my purposes? Sometimes, most times, but it's not always reliable. Use OP.GG and probuilds.com.
3.) The Game Itself
What are the different phases of the game? Laning/early, mid game, late game, AND UBER DUBER LATE GAME.
How do I know when one has ended and another has started? Objectives change. In early game, win your lane and try to push down your tower. Mid game, push down towers in all of the lanes, play around neutral objectives like baron/herald/dragons. Late game, win teamfight and get advantages with taking inhibitors. UBER DUBER LATE GAME is 50+ minutes. Everyone has six items or five plus boots. The death timers will be so long that whoever wins the fight will win the game, one hundred percent, so hold nothing back in a fight.
Can I prepare for a phase change in any way? Warding and rotations.
Any specific time landmarks I should look out for? (I know that buffs spawn @ 1:30; other than that, nothing.) Baron at 20 minutes.
How to avoid taking poke? Watch pro mid lane streamers, watch how they wiggle back and forth very fast to mask which direction they are going to move. Learn the cooldowns and range of their abilities and play around them.
How to win lane? Deny CS and XP by either zoning, poking out of lane, or killing them. Also, if you absorb jungle ganks without dying, you're wasting their time and can give your team an advantage just by going even.
Mid game? PUSH TOWERS. Seriously, just push up minion waves and hit the towers. Keep neutral objectives warded.
When to all-in somebody? Practice calculating their HP, mana, summoner spells, how much damage they can do back, how tanky they are, how close to tower or allies they are, if the jungler is nearby, and if the minion wave is really big. Early game, minion agro will destroy you in extended trades.
How to roam? Push in your lane first, otherwise you lose too much XP, gold, and tower damage, making it not worth it even if you do get the kill.
Ganking as a support? First make sure your ADC will be safe, then find a good path into the lane where you can cut them off and it won't be warded.
Is it worth staying and farming in lane rather than moving? Yes, almost always. Roaming is a risk and not guaranteed. If you leave, your laner getting free farm and tower damage is guaranteed. I'd recommend just chilling and not trying to force things until you've learned.
What is rotating? Killing the tower in front of you and then moving to a different lane and helping kill that one.
Late game? Get inhibitors down and then forget about trying to push that lane. Let the super minions push in, then when the enemy goes to stop the super minions, take a baron, towers and an inhibitor in another lane, something.
How to take objectives cleanly and safely? Use control wards. Also, don't auto stealth wards if they're disabled while you're doing objectives, as that gives vision to the enemy team. Just wait until afterward to clear them if you want. Plus, clear the vision plant so the enemy can't see and hit the blast plant so the jungler can't try to jump in and steal.
How to deal with fed players? Together. It doesn't matter how fed they are if they're dead, so try to save your CC or ultimate to stop them in a big fight. Most importantly, don't try to 1v1 them, because if they're fed, they're good at 1v1's AND now they have a big item advantage.
4.) Miscellaneous
How to know when to play aggressive or passive? Play up whenever you can. Play back if you just used important abilities and they're on cooldown. Play back if you're low on mana, HP, the jungler is nearby, or the midlaner is missing. You can also easily play back if the enemy minion wave is big, since it will push towards you and you'll get them all eventually.
Keeping level advantage? Always be farming something. As much as possible, don't let free minion waves get away.
Good uses for jungle plants? Use vision plants to scout instead of facechecking, discover if they are doing baron/dragon, and reveal stealth wards. Use blast plants to get away while running from the enemy, particularly over a wall. A tip for fruits, the crab will hoard one if nearby cuz it's tasty. Just auto him one and he'll scuttle away.
If I mainly play support, what summoner spells should I be using? Always flash. Never not flash. Ignite on exhaust depending on champ and matchup.
At what point does "full ap" become "too much ap"? When you die, you don't do any damage. Deathcap gives you more damage, but if Zhonyas helps you live longer, you end up doing more damage even though the item doesn't 'give' you as much damage.
Dealing with toxic players? Mute them, report if applicable.
On your own team (refusing to gank, refusing to farm, feeding deliberately) If your team is unreliable, don't rely on them. You can't change your team, so focus on yourself, improving and reducing mistakes. Nobody wins every single game, but if you perform well, over time you will win more often than you lose, regardless of the occasional 'unlucky team'.
On the enemy team (focusing that goes beyond the scope of practical gameplay, taunting, general scumbaggery, etc.?) Once again, mute. Sometimes, if you have a good, witty, and non-toxic comeback, take some banter and appreciate that you're playing against real people and not AI. If you're being focused 'beyond the scope of practical gameplay', then work on not dying and then the enemy team is at a huge disadvantage. If you keep dying, then it will keep being worth it.
Knowing when to ult and when to save? This takes practice, so for a rule of thumb if you might be able to use it, just go for it and eventually you'll get a feel for when it will make a difference.
The value of your life versus the value of your adc's life? You are worth 300 gold. If you die trying to save your adc and fail, that's twice the kills they enemy gets than if you never tried, so don't die for nothing. If your adc is on a killing spree, they are worth more gold than you, so from a logistic perspective, make that choice.
Is it worth sacrificing yourself to slow down a pursuer? Usually, no. You're worth more alive than not. Again, you are worth 300 gold too. Supports are not just for the ADC, they're for the whole team. If you can 100% get away, do that. Hopefully your adc will learn to position better. However, you should also usually be helping your adc avoid that situation with wards and pings.
Is pocketing a thing in League? Yes, especially with 'true supports' like soraka and janna. It's not always ideal, but sometimes is.
Should I focus on supporting one player (e.g. my adc) or should I try to peel for any player in trouble? The reason the support goes bot with the ADC is because they need the most help early game. Once you get to late game, they're the most valuable person around and need the most protection. As the support, belong to the whole team, not just the adc. They usually need the most help since they're big babies, but in a teamfight don't ignore the others, especially the midlaner since they are just as squishy and can put out just as much damage.
TL;DR:
What is my job? Use the strengths of your champs to support you team. It's different for every champ, from engage/cc like Blitz and Leona, to shields and heals like Janna and Lulu, to mage supports like Brand and Zilean, to tank supports like Sion and Malphite, to inbetweeny supports like my favorite, Bard.
How to manage that job and multitask effectively? Practice. Look at the minimap. Research. Check the minimap. Ward often. Glance at the minimap again. Work on your mechanics. Then watch the minimap again because that Jungler is gonna show up somewhere.
How to know when my job isn't being done right? If you're dying some, that's okay. If you're dying a lot, you're either going in at the wrong time, standing forwards too close to big bad guys, or not having the situational awareness/wards to avoid a bad situation.
What are my priorities? In reverse order, kill the nexus, kill the nexus towers, kill the inhibitors, kill the baron, kill the towers, kill the dragons, kill the enemy, kill the minions. Those last two are a bit subjective and swappable.
This paragraph is only for those that read through this whole thing. The most important advice I can give you is to relax. If you get tilted, go for a walk. Enjoy the nice weather. Hear the birds sing. Smile at a stranger. Drink plenty of water. Ask a friend for a book recommendation. Call your mother, she deserves it, will appreciate it, and you'll be better off for it. Brush your teeth twice a day. No really, and don't forget to floss. Change your pillowcase at least every month. Invest in comfortable shoes. Sit up straight. Drink some more water. Don't sacrifice sleep for anything on a screen. Find people to love more than a video game. Only when you truly enjoy your life without a video game will you truly be able to enjoy your life with it. That's what this is all about after all, enjoying a video game. I get that you'll enjoy playing more if you're not getting stomped all the time, but don't take it too seriously if you don't win. Lose is improve, but only with patience and practice. Best of luck my friend, you're on the right path to improvement.
[galio-happy]