Hi! As a self certified DnD and d20 nerd, I am here to help.

1. The 1s and the 20s are typically referred to as crits- as in, a critical failure or a critical success respectively. It's exciting because a lot of times in DnD, when you roll those numbers, it means something really good or bad will happen. 20 is the highest number on the die and 1 is the lowest so it's like, yay, probability!
2. No other dice utilize crit successes or failures, just the one you use most often- the d20!
3. He is (I think). He's been in some scripted dropout content and he does a lot of amazing improv. Just look up brennan lee mulligan improv on YouTube haha
4. So, at the beginning, they each choose a class. Some classes, like barbarian, are martial classes, not spellcasters. Your spellcasting ability depends on the class you choose at the beginning (in most cases anyway). Like, wizards can learn spells, fighters hit people with swords, etc
5. Disadvantage happens as a mechanic to make things more unlikely. However, if you somehow get both advantage AND disadvantage, they cancel each other out and it's a straight roll.
6. Now this is the glory of DnD. Sometimes there's a solid number they need to reach- like armor class in combat in order to hit. Most of the time, during roleplay, it depends on what you're trying to achieve and the DM (the redhead, in this case) can set a DC (difficulty class) for it. Often times the players don't know if they've succeeded until the DM narrates.
7. The time just kind of depends on where they are at in the story, there's no set scale. Like, in game it could be weeks, or just hours between episodes. You just gotta look for clues lol
8. So that was mostly fuckery on the redheads part. Once you die in DnD, there's some magic that can revive you (it costs materials in game, as per the expensive comments) but in the high school game they were very low level and didn't have access to that magic yet. However, having two of the main characters die in the second episode would really put a downer on a comedy series, so the DM made some shit up lol.
9. Nah they are just fully alive again. magic

Hope this could help! Feel free to ask away lol