What's "turn up" mean? I see this used in hiphop a lot.

What does he mean by saying this?

He says this because Snoopy wants to dance. Earlier in the video, Charlie tells us that Snoopy loves life so much that he doesn't know how to express it. Saying that Snoopy has an obligation to his feet means that he has to dance to express his happiness.

What does "bail" mean? How can I use this word?

In the casual context, to "bail" means to cancel plans or break a promise to do something, usually without giving much notice. When the speaker says "I bailed at the last second," he means that he cancelled very last minute. Ex: She bailed at the last second, making everyone else very upset. Ex: My pet peeve is when people bail at the last minute.

What's "off" mean here?

Here "off" means "not quite right." For something to be different than usual, but with a negative twist. Here he's saying that he knows it's the same office, with the same people, but something isn't the same as it was - but in a negative way. Ex: Something's off. Oh! The painting is skew. Ex: I'm feeling off today. I'm not sure why. Maybe I should take more vitamins.

What's "messed up" mean here?

Here, "messed up" means to have made a mistake or done something to get in trouble. Ex: He messed up the whole project. Ex: She messed up when she forgot to lock up the store. Ex: Try not to mess up again.

What's "mazel" mean? Can I say it in other contexts?

Good question. This is a Jewish-American wedding, so they are using Yiddish words here. "Mazel" means "congratulations" or "good luck". People might also say "mazel tov." These aren't really words that are used by non-Jewish people. Ex: Mazel, man! I heard you got a promotion! Ex: Mazel tov on your wedding!