Does it need to be one play through?  Does it include katey?

No it doesn't include Katey and I'm pretty sure it's to be done in one play through, not sure though. I found it really easy to do by just not killing any zombies that I don't require to kill and just racing to the objectives, you can also pick up Sharon, since she walks slow, to save time (something I didn't do).

Yes and yes. Here's a video if you don't know the locations of all the survivors. 

Yes, it has to be in one playthrough for any of the achievements that say something about collecting all of... or whatever "all" you have to take care of. 
 
The survivors one can be tricky.  Just remember that you can pick up and carry Sharon, which took me a whole playthrough before the prompt to carry her popped up as I abandoned her, Tina, and Nikki because I needed to get on my bike and ride off.

Remember, the last one only unlocks after the final boss. That screwed me up the first time.

" Remember, the last one only unlocks after the final boss. That screwed me up the first time. "

This wasn't nearly as hard as saving all the survivors in a given day in Dead Rising but it still took me a couple tries to get all the timing right.  It seems like there will be infected survivors in Dead Rising 2 and finding enough zombrex to keep them alive will be part of the challenge since if you look at the notes or whatever section of shows survivor status has a section for turned survivors.  
 
I would have liked to see something a little bit more challenging in case0 but for the scope of what it is it doesn't bother me that saving all of the survivors wasn't crazy difficult.

Yeah, it wasn't too hard after once I figured out that I could pick up Sharon. She goes a stupid route which can fuck everything up. Also, go to the Diner and mix some food and get a couple of Repulse, that way they wont bother you.

I downloaded it and not played it yet.  I'm still curious about the unlimited time glitch.

" @RichardLOlson:  No survivors spawn using the unlimited time glitch, so doing it to get achievements won't do any good except for getting PP and killing zombies. "

Keep in mind certain survivors wont appear until certain times. They're really easy to get.

Getting most of the survivors is a cake walk. I've played through Case Zero a few times now and all of games but my first sometimes it will glitch and he won't tell you about survivors so you just need to know around the times they show up and go get them yourself.

" Yeah, it wasn't too hard after once I figured out that I could pick up Sharon. She goes a stupid route which can fuck everything up. Also, go to the Diner and mix some food and get a couple of Repulse, that way they wont bother you. "