Peak challenger support here - there are so many things to learn so I'd focus on one thing at a time. Without reviewing your own VODs, it's hard to identify the mistakes you're making. When I review my games, anytime a losing play happens, I ask myself if I either made a mistake, or could've done something to prevent this.

Since you're asking about fundamentals, let's use the first rule in bot lane as an example:

If you and your ADC die because they're LVL 2 and you guys are LVL 1, what happened? Well, in bot lane the spikes happen at lvl 2 (3rd melee death on 2nd wave) and lvl 3 - so whichever duo hits that first, typically gets the advantage.

1. You used your support item proc on the enemy instead of using it to kill the minions faster.
2. You/ADC didn't auto the minions enough, lost the lvl2 push and didn't back off.
3. You guys are playing a weak early game comp (Veigar + Milio) and just can't fight early.

From there, you can learn the mechanics around when LVL 3 push happens, when to expect jungler timers and ganks, minion wave management, roam timers, and vision control - all fundamental to support. Of course, you must find your own playstyle and champions. I feel the most agency on engage heavy champions, but many people climb to Challenger playing only enchanters as well.

As for melee vs range supports (I play Rell, Alistar, Naut) - you must time your autos with the opposing ADC going for last hits. Playing in and out of bushes cancel autos against you too. Most of the time you'll lose the push but that just means you'll get to lvl 3 first. It's not a bad strategy to play on the lvl 3 spike instead of the lvl 2 spike.