Ok, I just played Kayle 
with klepto and was doing terrible in early, but I got one of those elixirs of skill 
that give you an extra level. By the time I reached level 10 the game thought I had reached lvl 11 and was ranged. Later on I got an other one, and when I reached lvl 14 it thought I was lvl 16. Should this happen?
Kayle gains her passive upgrades based on how many skill points she's used, not her current level. You can test this with the practice tool
It's intended and exactly how the passive should work if you read it closely. People have been playing around this already.
Whether or not it's balanced is another question.
It's probably due to how the Ascension is coded.
If you look at it, it doesn't proc on levelling up, it happens once you level up your ultimate which means that skill point elixirs will trigger it earlier.
I don't know if Riot intended it to work like that but this might be the case or they wouldn't have bound her "passive" to her ultimate skill points. Might also be that they didn't take that in consideration and went along with it because it worked better with the coding.
Its based on skill points used, not actual level. If you don't put your first skill point in at level 1 you won't gain the bonus attack speed.
TBH I wouldn't mind removing the skill pot, its a little TOO strong for an RNG item
This is definitely a bug and you should report it, sounds pretty broken.
Yes, it is intended.
Strange, because I tried the same thing and though the animation happened, I still wasn't actually ranged til lvl 11... gonna have to test this out
It's not a bug it was intended it was pointed out on reddit and upvoted to the front page a week or 2 ago.
I believe it is intended.
Kayle's passive isn't based on her level, it is based on how many skill points she has spent. Normally that doesn't make any difference, except if you get elixirs of skill.
