All of this is good and means you're actually learning how to play the game. Keep it up! However, I'll address everything that actually matters as far as improvement is concerned:
Thanks for the advice! I'm not that good though. Hell, I'm not familiar with push or team fight compositions yet. It's just whatever people pick, which tends to be 4 carries.
I talk a lot since I'm the type who prefers understanding the theorycraft before I apply it rather than learning on the fly. It's what made Starcraft, which requires a ton of theorycraft, come naturally to me. Unfortunately, LoL guides are really lacking explanation on a lot of concepts and there is no replay system to review games, so it's difficult to tell if the conclusions I reach are correct and when I actually get better. Winning doesn't mean I got better; it could mean that my opponents were just horrible.
This a million times. If you main a tank at your level, your team isn't going to know how to use you. The enemy team, which is probably built with more tanky DPS, is going to have it's way with your team. Try champs like Renekton, Xin and Udyr. They can absorb a beating, and therefore help keep their teammates live, but they also deal a fair amount of DPS, and have decent pushing power, so you can kill the enemy and push to tower afterwards. The bottom line is that very few people at your level of play will be able to use Ali to his fullest abilities. He's an amazing tank, but he needs a team that knows how to play with him.
I actually tried off tanks before I played Alistar. Off tanks/tanky DPS need a lot more farming than I'd prefer to be useful damage wise since most rely on Trinity Force and other expensive items. Most guides recommend solo top so you get all the last hits, but the chance of a team at my level having a good jungler/roamer is pretty low, far lower than having a good mid carry.
There's also how I'm always gold starved. Unless my laning parter refuses to last hit, I tend to leave minions to them and zone while camping bush. After I get my boots of mobility, partner permitting, I tend to spend more time attempting a gank or rushing to hold a tower until a teammate returns. It gives me little opportunity to stop and kill minions again, especially if we kill their first towers and there's no safe way to farm without overextending. I guess there's jungling, but even then I find that I'm much more useful when off helping allies in group fights. I don't scale that well with uber items anyways.
This makes me think you should try Xin Zhao. His placing is somewhere between Ali's and Yi's. If you go tanky, you can shift around the front line and take enemy pokes, while waiting to dive through the team to get to the carry. If you go DPS you can snipe anyone in the game off, as long as you get them alone, and if you dive in at the pivotal moment you can swing entire team fights by yourself. His abilities are also very simple, yet they syngergize well together.
I'll try Xin Zhao when he becomes free. I've laned with a bunch of them. I'll totally miss Alistar's headbutt though. I'm actually eyeing Singe when he becomes available because the flip is hilarious.
The main issue here is practicing. Try to keep track of how much damage your allies are doing, and focus on last hitting around them. Zoning is all well and fine, but if your ally isn't last hitting, go ahead and take them.
I do try to last hit at towers. I like how Alistar's attack animation is pretty damn quick, so it's a little easier to hit from under there. The hardest part is the combination of multiple factors making it hard to decide if a last hit is even possible. I need to determine it early so I can move Alistar in position to last hit; his movement speed is slow as hell without boots. If I guess wrong, I'll not only miss that but also be out of position for another last hit.
Ali built pure AP can pack quite a punch, and drop giant heals on his allies every 3 seconds.
I build support Alistar, little to no AP. Support Alistar fits me better than pure tank or off tank Alistar. Teams aren't good enough for me to try jungling, much less roaming, so those aren't options right now. I tried a bunch of guides and support really fits me best. Mainly because that way I won't feel completely useless standing around if initiating is a bad idea at the moment. It helps that support Alistar has plenty of mana regen for a reasonable ability spam.
After the massive nerf to his AP ratios, the general consensus amongst the guides I read was that building AP was now useless. Following that one mobafire guide, I focus on CDR, Health (armor/magic res don't synergize nearly as well with his ulti), and auras that help allies. With 40 CDR, his ulti is enough for tanking since it lasts just long enough for me to get one last pulverize/headbutt off (ulti lasts 8 seconds, 40 CDR pulverize has less than 8 seconds of cooldown). That will either catch a fleeing opponent if we're winning, tip the scales in our favor if it's close, or save an ally if we're losing. I just pop the ulti when I hit around half health.
Following that one guide, I actually open with Mana Manipulator. So, I take care of my partner's health and mana regen during the laning process while attempting to zone to deny enemy last hits. If the opponent overextends, I go for the kill. If not, I try to find opportunities to Headbutt harass while their partner is out of position to punish me for it.
Anyway, you're obviously on the right path. Alistar is an amazing tank, and can completely destroy entire teams if your team can use him well. Just expect a long, cold winter before you get to that point
I've been doing ok so far matchup ratio wise. It's more important to me that I learn after each game rather than grind my way to 30 quickly. Although playing a tank has given me more insight into the mid and late game dynamics, I'm still worried about the early game. From what I've observed, doing well as a tank early game builds your team's confidence in your ability to initiate, which means they're more likely to actually follow in a team fight later.
I've learned stuff the hard way like never initiate in jungle unless your team is more melee focused. Ranged squishies get destroyed there. I've learned to never initiate if I don't have a good idea of where the enemy team is. Being too far deep initiating while the squishies are flanked is bad. Doing the flanking myself is a given if my allies are grouped together and chasing. I've learned to check to make sure the primary carry is committed to a fight before initiating since I really need kill power if Headbutt isolation is going to work.
I also rely on Shurelya's a lot now for initiating and/or chasing. It has the lowest cooldown amongst my three options (Shurelya, Ghost, Flash) so it's much more spammable. I just make sure that I'm out of combat for 5 seconds for the boot speed boost, which combined with Shurelya gets me enough speed to close in range suddenly. Doing a bunch of run back and forth earlier masks the movement well enough. I forgot to check if using Shurelya's and/or Flash activates Trample. If not, I'll need to start casting Triumphant Roar right before so I can run through everyone.
I've also learned to be more aggressive with my 3 initiate options and my ultimate to the point of tower diving if the opponent is around half or even 3/4 health for squishier opponents. I hate having to use summoner spells and my ulti to escape instead of an initiate. It's better to try for a kill now, at worst forcing the opponent back to heal and opening up the possibility of a tower push, which also gives my initiate options time to recharge since I've delayed the team fight with that pressure. How aggressive I am usually depends on the team though. If I'm not confident in my team's ability to kill an isolated enemy quickly, then I won't initiate and instead will hold back my spells to save my allies in team fights. I still remember that nightmare game where I would Headbutt isolate an enemy Katarina and my allies were unable to kill her off quickly. So, she pops her ulti and kills half the team. Ugh.
There's also the Alistar specific stuff I'm learning. Deciding on whether to use a summoner spell to get in front of an enemy -> Headbutt -> Pulverize, or using Pulverize to set up a Headbutt possibly with a summoner spell first to land the Pulverize, or using the Headbutt Pulverize combo.
Deciding who to focus I'm still learning. Between an out of position AP carry who isn't that well fed versus a well positioned and fed AD carry parked a bit further back, which is more important? Taking out the AP carry is practically guaranteed, but then I risk the AD carry destroying everyone while my CCs are on cooldown. Taking the fed AD carry means I might need to pop another initiate just to get behind her, and even then it might not push her out far enough for a kill, but killing her means that my team is more likely to win the fight. It's the same with a Healer on the enemy squad. Is it worth targeting the healer in case the healer is too good at clutch saves? Or is the burst enough that healing doesn't matter?
There's also figuring out when to save CCs and which ones to save when initiating. My general thought process is that if my team kills fast enough, I'll pop my CCs on initiating instead of interrupting channels. If channels are that big a problem, I'll just use Pulverize and save Headbutt for the interrupt. If there are multiple channels...
I'm still trying to remember to glance at my team's portraits before each initiate. Headbutt isolating an enemy to my team won't mean crap if it helps them chase a low hp ally down, which I've done several times. Headbutt isolating an enemy is also dumb if my allies have no mana.
I still haven't figured out when it's advisable to travel through the jungle to get to places. I've gotten ganked there more times than I like, forcing me to waste a summoner's and/or my ulti to escape. Part of that is not knowing when to buy Wards. I know to buy Invisible Wards against Evelyn early, but beyond that I don't know when it's a good time to ward places. I've been meaning to try purchasing them after I hit 35% CDR, but I don't go shop often enough. I'm usually wandering out there, making sure that my allies don't die needlessly. Maybe I should buy some right after boots (can finally move around) or Shurelya's (most important item after boots since it's my 3rd initiate). That way I won't have to make an extra trip to the shop. Hrmm.