These are just my opinions on the things you mentioned, hope some of it is helpful, i trued to organize them a bit so its easier to skip thro this post (i know i type too much and that i suck at typing :C sorry)
---CS'ing-----
you can practice in a custom game
5 to 10mins, my friend had me do this w/o using any abilities or buying items or pushing the lane and had me record my cs score or each round, i saw a small improvement in the rounds (tho i main support so its not that big of a concern for me to know how to cs)
you can google it, some ppl have even more elaborate variations (using abilities > to no abilities > to looking at mini map while doing it > to doing all the steps w/ a bot in the game) the final step would be to take your new practiced skills into a real game and see if you improved on cs'ing
ive also heard people say that you should do these kind of excesses with the champion you wanna get better at last hitting cause everyone has diff animations and damage that can effect cs'ing
---Champs/Role--
focusing on one champ is good but you probably should pick at least a role and maybe even a sub category with in it you wanna focus more on cause most roles will have similar skill sets to focus on (for a support you should learn when to ward and where, while w/ a diff role that might not be the top priority, when should you dive for the adc as an assassin or when should you not cause it will result in your death?, etc)
for the longest time i would not play anything but Annie cause i felt like i was bad w/ this champ why should i move on? I did eventually move on but at least some of my friends seem to really respect my Annie (even though i still think i suck) iv even had comments like ".. ur going annie mid right..?" in ranked cause i did such a good job last time xD Im confident i can carry as mid in bronze elo or at least get supper fed but silver and up idk i can at least stay even in lane for the most part :)
You dont need to commit your whole life to one champ but if you would be willing to pick one you really like at the moment and spam the fuck out of them and on the side also read guides about the champ, watch videos, see what mains of that champ do, it will really help you be better at that one champ beyond the just "their combo is this and i max in this order". Ive recently been doing that with zyra for the past month and even now i feel like im still learning new things about her and understanding her on a better lvl, iv managed to improve my win rate with her in ranked (which im supper proud of!) to almost 55% (look up CoreMilitia, its my other account)
----Norms vs Ranked---
I dont think you need to play ranked per say to get better, for the purpose of learning (which is how you improve) norms are good enough, you can even do draft pick so its a bit more like 'ranked' in the idea that the other person might chose to counter you
i had a month where i would play a lot of ahri in norms on a lvl 15 account (i did not feel conformable going vs 30's due to how little i play mid being a support main and all + i kinda have anxiety XD) and i would try some crazy things w/ that champ (like practice flash charming) and just things i would have not been comfortable doing on my main or in ranked ahahha
if you have silver friends you can duo up with in norms you might find your self playing vs some silvers which might be a hard match up so i dont think ranked is necessary the only option to learn and get better (and the same applies for if you play norms with a gold ranked friend and so on) i actually made friends w/ a dim players in norms cause i was duo'ed up w/ plats and golds ^^; (he kicked out butts pretty hard that game)
----Other Tips---
i hear a lot of people say that watching streams is a good way to learn (but i would not know cause i dont do that)
also watching replays of your own games, you might notice mistakes you made that you dont always realize in game (use for example replay.gg)
Its hard for me to give you specific advice cause iv never played w/ you, so iv never seen what your bad habits might be so all of my info/tips is pretty general :/
Other then that one of my favorite quotes that i found on reddit one day:
When a bronze player dies they way "wow my team sucks at this game"
When a diamond player dies they say "wow i suck at this game"
In short, you need to recognize what you are doing is wrong and then focus on not making those mistakes in the future :3c
even if you team mate is shitty bad, always ask "what could have i done better/differently?" as a support main i dont always get a fantastic flawless adc and i have to ask myself what do i need to do, build, and how to ward to keep this idiot from killing himself? XDDD or sometimes im the one making mistakes and then i ask what do i need to change about my own actions/positioning/choices to improve the lane :)
Good Luck!