What does it mean if the phone does half a ring before going straight to voicemail? So many times, I'll call someone (iPhone to iPhone) and the iPhone will ring once, but goes to voice mail immediately about halfway through the ring.

What are the possibilities? I'm assuming the phone is dead could be one, but I know that's not the case. Maybe they could also be on the phone?

Then I'll call 10 minutes later after they text me back saying "whats up," and it rings normally. I figure they must have been on the phone? But I thought it normally gives them a choice whether to drop the current call or not, so maybe that'd take more time than half a ring?

I called 3 times, and all 3 times it rang half a ring, and went to voicemail.
Half a ring means that the phone received the call, but instantly declined it. I've only seen this behaviour with the caller blacklist, or the do not disturb mode ☽...  In your case, as the person you called seen your call,  it means that it's the do not disturb mode that caused this