Why did der Tod bring Elisabeth back to life when she fell from the tree? If one takes into account his character as he describes himself in the Prologue, and even in the rest of the play wherein he makes clear many times that he wants Elisabeth to be with him (and stalks her and her family when not trying to woo her in his morbid way), it does not make very much sense.
In the versions with the extra song for der Tod in the first act, he says that half his problem is that he loves her as she is, vibrant and alive. Taking her with him would ruin that, so instead he stalks her to win her.
In one of the versions I've seen (one without "Kein Kommen Ohne Gehen") Elisabeth says something to der Tod just as he's about to kiss her and take away her life. Maybe this affected his decision?
In the Takarazuka version Elizabeth begs Death to send her back upon realizing that he is about to take her.
Why is der Tod in a dress during the Mayerling Waltz in some productions? Is it to signify that technically he's sexless, or just because?
He represents the Baroness Mary Vetsera, Rudoph's 17 year old mistress who died with him in the murder/suicide.
What exactly happens to Elisabeth after she dies? One can gather from the prologue that she isn't there with der Tod, but other dead people are, and she went with him when she died.
She's definitely there in the Essen prologue staging. For a lot of the others, it's left up to interpretation where she is. Presumably she is somewhere in the world of the dead, just not the part we see.
Generally, the main protagonist doesn't appear in opening numbers of musicals (Wicked, for example, where we don't meet Elphaba for until the second number) in order to establish how this character has impacted the world and set them up.
Maybe she's wandering the world of the dead as she did in life? We see in the show that she was restless and wanted to stay as far away from the Viennese court for as long as possible.