Kled and Invisibility/Stealth abilities

How is Kled affected by someone with stealth abilities? My main question here is mostly for Vayne and Akali, as they have (AFAIK) the fastest on-demand stealth abilities. If Kled Bear Traps one of those two, what happens if they immediately stealth after it hits? Are they revealed or not, does it stay on or detach, and does it still work if they're invisible?

In addition, if Kled marks one of those two with his charge and they stealth before he can use it again, can he still charge through them if they're invisible? Are they still marked, and are they revealed by it?

If Kled ults one of those two and it locks onto them, and they stealth in response, what happens? Is the ult negated? Does it continue in a straight line? Does it stop in place? Or does it keep tracking them even while invisible? Does the ult reveal them?

Also, a slightly separate question that I've never figured out: How does Caitlyn's ult interact with stealth? Does it just stay locked on?