Changed Beliefs

Questions

Heyo! I've been thinking a lot lately (mainly about quirks) and I have a few questions just in general, I don't expect answers I just wanted to share them with people that might actually care.

(I'll try to get the next chapter out soon as well)

Question 1:
What is One for All? I know it's the quirk Izuku uses and all, but is it the name for all the quirks the user has or is it the fact the user can transfer to another person or what? It's just confused me quite a bit.

Question 2:
How did the first user of One for All find out about his quirk? Because his quirk is passing his quirk onto someone else, but it has no physical evidence of even existing like Denki's quirk, or Tsu's quirk. So how'd he figure it out?

Question 3 (contains manga spoilers):
So Nana's quirk was float, and Izuku also has black whip and danger sense from other past users, and we know that All might was quirkless before Nana gave him OFA, so what is the main quirk Izuku uses called? And I'm talking about the green lightning that makes him stronger.

Question 4:
Who names the quirks? Is it the children or parents or scientists? Or is it implied that other people had the same quirk as these main characters (which would make sense seeing as there are a lot of people on this Earth) and they named them? And if that's the case how come we've never heard of them?

Question 5:
How tf did Hagakure get into class 1a? Did she just tell Nezu that he couldn't prove she didn't be the robots or what?

There's probably more questions that I forgot. Also sorry if this is either confusing or stupid, it's late and idk what I'm doing anymore.

Have a good day, night, or evening! Bye!