Simply put, I was wondering if for example, I had an account that got banned on LoL, would all other accounts that were tied to that e-mail address, also get banned?
Typically no, but in extreme cases it's a possibility. Unless you're one of the worst handful of League players to exist you don't really have to worry about that.
Nope. All punishments apply to the one account they were served to.
Riot has no official policy on multiple accounts, other than they cannot transfer RP or skins between them.
The only real policy for account usage is account selling, and account sharing. Fun Fact: I started League of Legends sharing an account, made an account eventually, gave up, and made this account nearly a year later.
The only case that I'm aware of that to happen to was Dunkey, and he straight out dissed the entire League of Legends platform. Which is fine, because he consistently showed abuse and had a monkey see Dunkey do following that mostly left with him.
You're free to make as many accounts as you want. I wouldn't recommend that you try to mirror Dunkey's example and create new accounts specifically to troll, and keep a main account as if it cannot be touched.
