what does 'stick around' here mean?

Is "baddest" same as "worst"? Are both acceptable?

"Who's the baddest of them all" actually references the movie "Snow White" - the evil Queen famously asks "who's the fairest of them all?" to the magic mirror every day. "Baddest" isn't considered to be standard English, the proper word would be "most bad" here to mean the degree of being "bad" that one can be. Although "the worst" could be used here, it doesn't sound entirely natural because "bad" in this context is meant to have a meaning similar to "tough" or "fierce," as the singer uses this expression to challenge or taunt her enemies. Thus, "toughest" or "most bad" would be more appropriate here. Also, note that as slang, "bad" is also used to mean "the best" or to describe someone who is physically attractive. Ex: She's not a bad kid, she just doesn't like to listen to others. Ex: Dang, she's fine. She's the baddest woman I've ever seen.

Can the verb "use" come after "did"?

Yes, the verb "use" can come after "did", although it is not necessary. "Did" in this sentence is only used to add emphasis to the verb "use". It is common to see "do", "does", or "did" in front of a verb to make the verb sound stronger. Usually, DO verbs are stressed when speaking to further emphasize the main verb in the sentence. Ex: A: Do you like my new shirt? B: I do like your new shirt! Ex: So, you do want to talk about it?

What does "crafty" mean? Is this word common?

"Crafty" here means "creative". A "craft" in this context is a creative project, which here is making different mechanisms for delivering Halloween candy to trick or treaters safely. Therefore, "crafty" here means "creative" in the context of making a "craft", which is a creative project. "Crafty" in this context is a known word, but it is not very common in conversational English. This word is mostly only used by people who regularly make "crafts". Ex: She is crafty, she loves to make jewelry. Ex: I am feeling crafty today, let's make something.

I think "forever" already means something that is continuous, but "forevermore" has stronger meaning?

Yes, you're correct. Forevermore is used to emphasize or exaggerate the period of time. It means "more than forever" which is, of course, not possible but makes the statement seem more dramatic. Ex: We will be together forevermore.

What's "fake out" mean here?

This is a bit of an informal phrasal verb. To "fake out" means to deliberately mislead or fool someone. In this song, the lyrics "heat waves been fakin' me out" don't necessarily mean that the very hot weather has been misleading the singer, but maybe that they are making him feel confused or abnormal. Ex: The defender faked me out and made me miss a goal. Ex: He's good at faking people out, be careful.