Just bought 9 avarice seals and 2 more avarice quints, now I'm between +4.35 and +7.35 gold per 10 depending on rune/mast page.

The most concerning is losing my -5% time dead quint but I think it's probably worth it for 1 gold per 10. The seals won't be missed as they were a general mishmash of primary per-levels. An extra 700 gold per 35 minutes should come in mighty handy. I play a no-ward no-elixir style, and on people where an item upgrade is not viable, I might actually be able to start using them.
Ryze has a habit of being shut down in mid because he's pretty short-range for a caster. He is a great mid against many opponents, and then worthless against others and you just need to call a lane swap immediately before it becomes a problem (or don't bother going mid if you see someone with range in the loading screen). Basically if the enemy can harass you without risk of you landing a prison combo, it's not worth having ryze mid. Annie is similar; limited mid application, but great against people without a ton of range. If the enemy is dumb enough to try and pump a kass or kat to 6 in mid, you will rofl at their fail, but most of the time you need someone with more range.
Tenacity and cleanse are kind of a waste on Yi IMO since he can instantly turn off slows, and it doesn't
prevent a meditate break. If that's a problem you can try a banshee shield. I've never thought about masteries since it's just a joke strat, but I guess I would go for veteran's scars in Defense and Mental Force in offense. With 23 points you can max Enlightenment and Sorcery and completely skip a 15% CDR item, probably lucidity in favor of swift, mobility, or sorc.
I'd like to get back into this, but I have basically no idea how to play DoTA/LoL
The biggest problem isn't the game itself so much as overconfident kids who think they know way more than they do and won't shut up about the millions of things that you're doing wrong. There's plenty of noobs to go around in the matchmaking queue so I wouldn't worry about skills.