1) It depends.
The idea of, say, "Santa", is more so about a mythical figure who gives gifts to those who have been good, and something poor to the bad eggs, and is the peak of a festive holiday season. In that sense, he holds no more weight than just another fun story to be told, that perhaps happens to be paralleled in a role-play's universe. The best part about that is that you don't even have to call it "Santa", you could make up your own lore concerning something similar for your universe, if you are the GM. The concept is still the same, and it isn't disconcerting.
I tend to abhor you if you bring in real-life persons to directly, unabashedly reference. And I don't mean dropping a few hints and similarities, I mean just outright having your character say something like, "I'm gonna name my Bidoof 'Justin Beaver'" or describing an encounter with President Barack Obama as he jogs his Shiny Furfrou named Bo. I personally don't like to mix fiction with real, actual persons. What I do like, and have done myself because I frankly find it punny and sometimes cute, is make a parodic reference, so that you may know who I'm talking about, but I'm adjusting them to fit the universe they are in. My favorite one I've done myself so far is having a Pokemon Trainer listen to "Smells Like Teen Mespirit" by a grunge band called Carvanha.
I mean, every generation, Pokemon mentions Nintendo's own consoles at the start of the game, so when it comes to video game pop fiction, I think it's fair game with that.
But that's in modern fantasy settings like Pokemon. If we're doing some realistic slice-of-life role-play, I would say it just doesn't matter.
2) In my experience, people who bring up canon characters to feature and control in their role-play... well, they tend to end up flat themselves. I don't care if the execution is good, but everyone has different standards. Some characters come from a background of extensive lore as well, so then you get into a big mess if some greenie comes in and tries to assert one thing over another. Concerning events, it all depends on the role-play's timeline. Otherwise, yeah, why not mention a little history to tie something together, or make a callback.