In the first situation, TT clearly is touching Crowder in a mocking, antagonistic manner, not a jovial manner, given the context of the situation. A technical foul was warranted.
In the second situation, OBJ broke the law, period. You are not allowed to put your hands on law enforcement officials. And again, this was done in a mocking, antagonistic manner. This is a very minor crime given the situation, but it's pretty cut and dry as to what it is. FWIW, I'm still angry my Giants traded him, despite the mini-spiral he's been in since he was traded. I like OBJ.
The third situation barely seems worth talking about and is clearly different from the other two. This was textbook jovial intent.
Butt-slapping doesn't bother me in the least. I never saw an issue with it and participated in that culture with my teammates and even with friends at times when I was younger. But I do understand you can't put your hands on another person if they don't want you to, as I expect the same right to tell someone not to touch me. I always did wonder, though, why some people are uncomfortable with a jovial butt-slap from a teammate or coach. What made them so uncomfortable about that?
In terms of 'PC culture', I'm much more concerned about infringement of speech than any sort of physical contact between two individuals.