Double Corrupting Gems

Hey,

I wanted to ask if I understood corruption, or specifically skill gem double corruption, correctly.

So a skill gem has 4 corruption outcomes:
- do nothing
- add/remove a level
- add/remove quality
- convert to the Vaal version


Is there an "add 0% Quality" outcome?
What happens when a Quality roll cannot happen? (For example, if you roll -1% quality on a gem with 0% quality)

Are these results all weighted equally?
Are adding and removing levels weighted equally?
Are these two separate rolls? (So one roll is "change the level of a gem" and then the second roll is +1 or -1)
So assuming the above questions are answered with "yes", getting an added level is a 1/4 * 1/2 = 1/8 chance.

Using a skill gem that has no Vaal version just removes the option, so getting an added level is a 1/3 * 1/2 = 1/6 chance, correct?

If you double corrupt in Doryanis Institute, you cannot roll the same category twice, correct?
So you cannot roll "remove quality" and then "add quality", correct?
And you cannot roll "do nothing" twice on one gem, correct?

So assuming the above questions are answered with "yes", getting an added level with a gem that has no Vaal version using Doryanis Institute should be a 1/3*1/2 + 2/3*1/2*1/2 = 1/6 + 2/12 = 1/3 chance, am I correct?

Thank you in advance and sorry for so much math :)
Best Regards
Swerik

So according to that wiki article, all of my assumptions are correct except for

"

Using a skill gem that has no Vaal version just removes the option, so getting an added level is a 1/3 * 1/2 = 1/6 chance, correct?

and therefore

"

And you cannot roll "do nothing" twice on one gem, correct?

Instead the calculation should be 1/4*1/2 + 3/4*1/3*1/2 = 1/8 + 3/24 = 1/4, am I correct?