For the first point, you could use a random generator and make it pick from a Gaussian or Poisson or other probability distribution depending on the situation.

Many RPGs that aren't so closely related to DND use a dice pool. Instead of like 1d20, you might roll 3d6. Now you're more likely to get an average result. Only one way to roll 3, but a bunch of ways to roll 10.

The nWoD games you roll d10s and count how many come up 8,9, 10. Very fast, and once you're good at a task you know you'll generally succeed. It's more a question of how well you'll succeed and how strong the opposition is.

I'm not mathy enough to talk beyond that, but I find it much more satisfying.

Playing under someone more experienced can build confidence, but the only way to learn how to run a ttrpg is to start running one. Find some one page RPGs with really simple rules that can be learnt in a few minutes and played over an hour or two. No one has to invest in anything, you can switch between different ones to find what people like, and there's no pressure to keep running a campaign if you find it too much. Once you have an idea of what it's like running a game you and your friends can decide if you want to play a long adventure.

I had a really fun game of Vampire back in like 2016. I'd love to have another go at that, or Mage. The dice pool system always felt simple but exciting. Characters started out competent and being able to buy individual skills or powers was more satisfying than waiting for whole levels.

I've heard good things about Delta green, but never looked into it.

Alas, my college days where "hey you look nerdy you wanna play vampire?" are long gone.