Would a story with a focus on both science fiction/alternate history and fantasy elements be called fantasy or science fiction? I realize that urban fantasy as a genre blends a modern setting with fantasy, but would it still be called urban fantasy if the technology was different/more advanced compared to modern day? Personally I think it would be, but I'm not completely sure.
Who cares what it's called? Write it, make it good, and leave it up to others to figure out what category it fits in, if any. If a story doesn't fit in a pre-existing category, it probably means it's pretty original. And that's good.
I'd call it science-fiction/fantasy. The alternate history, to me (without knowing the exact context) seems to be an element of science fiction.
Depends on the publisher you are trying to sell it to. Assuming it falls enough within that publisher's genre to be a candidate, label it according to how that publisher would label the story. If it's too close to call, call it sci-fi/fantasy. The publisher may recategorize it in any case. Genre crossovers can be harder to sell in any case. If you don't care about selling to a publisher, it doesn't matter one whit how you choose to categorize it.
I agree with Cogito. But in any event, I would not consider "alternative history" to be sci fi. Philip Roth's "The Plot Against America" was definitely alternative history, but it was definitely not science fiction.