I have been playing for a month, am terrible, and don't know how to improve. Please help.

Warning: long post, TL;DR at bottom.

Hello veterans of League.

My roommate has been playing League for some time, but I've never been interested until recently. I play some casual Starcraft, Diablo, etc., so I am not new to the visual style/controls of the game. However, I have never played a MOBA before. I was looking at fanart online and found some cool pieces for League champions. I thought Azir's design was the best, so I decided to try the game. I was not discouraged by the high IP cost of the character, and played against AI using the free rotation until I accumulated enough to buy him. I have since gathered that this was a terrible idea, but it worked for me at the time and I don't regret it.

I find Azir to be very squishy at all stages of a game, but he is still my favourite champion to play. I have tried many of the champions on free rotation (Riven, Ryze, Lux, Ashe, Tahm Kench, Sejuani, etc.) and found that I prefer ranged characters over melee. Mid and support are my favourite roles, with Janna being my go-to for the latter once I discovered her from this week's rotation. I also liked Lux in either role but don't have enough IP to unlock her yet.

Obviously, when I started, I died a lot even against AI, so I practised until I would die 5 times or less per game before moving to blind pick PvP. I think I was level 10 or so. Since then, I have played mostly PvP unless I was trying out a champion that sounded complicated. I know that one of the most important things for a beginner to learn is how to last hit, so I have focused on CS more so than on trying to kill the other midlaner (1/3 of the time Yasuo). I also know that not dying early is important, so I tend to play very safe near the turret and always try to keep one of the river bushes warded. A piece of advice I've seen somewhere is to look at the minimap every time I last hit a minion, and I try to keep that up. For runes and masteries I just look up what's popular and make my best approximation.

I don't know about you all, but I encountered a tonne of flames and not that much constructive criticism in those PvP matches, often despite telling my teammates that I am new. The friends I play with in premades are: -"Sona," who is also new at the game, prefers support/adc, and is already discouraged by the amount of flames; -"Cait," my roommate, who only plays blind pick and adc; -"Nocturne," who stopped 2 years ago and just got back into the game. I play about 1/3 to 1/2 of my games in a premade, and the rest with randoms.

I can deal with being killed repeatedly under my own tower or as I attempt to ward a bush by champions I've never seen in a game before, let alone played against. (If there is a way to look up an opponent's abilities while you are in a game, let me know. That may prevent one of those 1/10/2 games I get every so often.) I can deal with 5-game loss streaks and being told I'm terrible in myriad ways, because I know I'm terrible and am focused on just CS and not dying for the moment. The problem is, I'm level 26 now, and my (level 30, bronze, or silver) teammates seem to expect even more skill/game knowledge that I don't have. For example, I used to take cleanse because it gets me out of trouble, but people tell me to take other summoner spells and I don't know why. Also, I try to do damage to the opponent's tower when the other midlaner is elsewhere, but apparently that is incorrect as well, and I'm not sure what I should do otherwise. The list goes on. I don't want to keep enraging my teammates even though I personally have fun because I am practising the champions I like.

TL;DR: do any of you experienced players remember how you managed to climb over the brick wall of a learning curve I am facing at the moment, if you have had similar experiences when you just started League? (Is my pigeon prince Azir the problem?) Any advice is appreciated.