When does a 'tickle' become a sexual assault
In general I think it's a tough question about when a lot of things become abusive, but here I think it's firmly as soon as it's being done for sexual thrill. Even if it's a "normal" tickle that's being done for sexual gratification, I think that is at least molestation. As soon as you are using someone (with or without their knowledge) sexually in a way they haven't consented to, that is misconduct whether it's classified as rape, sexual assault, molestation, whatever: it's all still very wrong. In general I'm not a big believer in "victimless crimes", but I think kids can read emotions in a room pretty well, and there is always the possibility they are picking up on what's happening. The fact that they may not realize it happened makes it no more moral than having sex with someone unconscious is than while they're awake and protesting.
When does correcting a child in front of their friends become humiliation and shaming?
Here I'd say never, if it's just done when they do something wrong. If their friends are over and the child decides to throw a tantrum maybe (I'm assuming they are pretty young), I don't think there's usually anything wrong with sending them to their room and cutting the play date short, or giving them a time out, or whatever discipline seems fit. If it's the same thing you'd do when you're alone then you're not embarrassing anyone, and it's good to be consistent and (especially for young kids) to give out the consequences soon after the infraction. If the kid is older, then I'd probably not generally discipline them in front of friends unless it's something particularly bad like theft. Really though, I think if you do the same consequences around friends and alone, it's generally not abusive (unless of course the consequences are abusive in themselves).
The other two are gradients. I think as a parent I'd avoid any sort of physical punishment just so it doesn't turn into a beating, but I don't think everyone who has spanked their kids are awful parents. Besides, you can certainly punish kids in abusive ways without beating them, like when does a time-out turn into abuse? One minute? Ten minutes? Twenty? An hour? Ten hours? I'm sure most people would fall somewhere within the first and last time limits, but it's pretty vague and I think most people would be unable to put a minute on it, and you'd get a million different answers among those who could be specific. In the end I think it's up to the parent to see when their kid is clearly in pain from the punishment and to lay off it.
As for independence, I think that's probably the toughest one. You'd find a ton of parenting books all advocating different levels of care, and huge debates in psychology about that subject. Generally being around to provide emotional support when the child wants it (within reason) and giving them all the necessities for a safe (to the best of your means) life is probably a good minimum.