First of all, congrats! This is really exciting! I totally understand your being nervous, but I am SURE Rosie, no matter what her initial reaction, will end up loving having a pal to "pal around" with.
To address your questions:
1) It is not cruel to keep two cats in one room together during the day as long as there is some room for them to romp around, plenty of things to keep their interest, and cozy places to nap. If there's a window, do you have or have you considered getting a Kitty Perch for the windowsill? Or a small cat condo that's just tall enough so they have a place to sit and look out? Gary and I live in an RV that's 40 ft by 8 ft - and we have five cats. But we took out the "dining room" to put in cat trees/condos, and we have the place filled with tubes (to run and play in and create different levels), we've emptied out overhead cabinets to create vertical space for them, and they have lots of toys that we rotate on a regular basis (every couple of days) - because they do get bored of some of the same toys if they're out all the time.
2) I would not leave them together initially until they're used to each other, and you've seen them interacting together and you're comfortable that there won't be (much) fighting. It's usually easier to introduce a kitten into a home than an older cat. There shouldn't be a problem with "who's alpha." Kittens can be annoying, however, we've found that the older kitties are pretty tolerant! Shelly even sits and purposefully waves his tail around (at times) for Flowerbelle to play with.
Just make sure you don't confuse play with fighting. It may look like they're going at each other, batting paws, "biting," etc - but unless tails are puffed and/or ears are flat back, it's "mock" fighting or play, and that's just fine and quite normal. Poppy might puff her tail (Flowerbelle does all the time), but unless Rosie does, I really wouldn't worry too much. It's really the ears flat back that's more of a concern.
So, bottom-line, I'd give it a few days or few weeks even, if necessary. But you'll have time in the evenings and hopefully on the weekend. The best would be if you bring Poppy home on a Friday night if you don't have weekend commitments. That gives you some time to make intros. And if Rosie's OK with it, no need to separate them for an extended period of time. We did it all wrong when we brought Shelly inside. Lazlo and Shelly, we thought, were going to kill each other. They were the same age, however, which really is quite different. But we left for several hours to take Gary's mom to the airport - and we came home to find them curled up to sleep together.
Never had a problem after that. Shelly established he was alpha, Lazlo sulked a bit for a few days, but once the order was established and Lazlo accepted it, everything was just fine and went back to normal around here.
You can leave kitty in the bathroom with a small litterpan, snuggly bed and toys. That's where all of our kitties "live" initially when we're not around until we're sure the bigger kids are OK with them and we're comfortable leaving them alone together while we're out.
3) Yes, you need two litter pans. It is likely that they both will use both pans, but ideally there is one litter pan per cat in multicat homes.
4) For feeding the kitty - how large is Rosie? What we did (until Flowerbelle got too big), was take a large opaque plastic storage box (the kind that's easy to find at Walmart) and cut a small hole in one corner of it. The hole was large enough for kitty to get into, but not large enough for anybody else to get into. We put kitty's food in there. They learn quickly! But the storage box has to be large enough that Rosie can't reach the bowl if she reaches her leg in there to fish around. That way kitty feels safe. Depending upon Rosie's size, that should work for a few months. After that, Poppy will have access to Rosie's food during the day, or Rosie will have access to Poppy's food during the day (whichever way you decide to go. If Rosie's round, I'd leave her food out. If she's thin, I'd consider leaving Poppy's food out) - not much to do about that. But you can take Poppy into the bathroom to feed her her food separately when you get home and through the evening and before bed. That was our solution. Others might have better suggestions. Flowerbelle likes her food better, so we free feed all the cats, but when Flowerbelle wants her food, she meows at the bathroom door.
Just remember, give Rosie lots of extra attention and plenty of alone time (I mean alone with you
)! It's probably best to leave Poppy in the bathroom while you're at work for at least the first few days. Rosie will know there's another cat, they'll be getting used to each others smells, especially if you rub each one of them with a towel every morning before heading out and leaving those towels under the food bowl of each. They'll come to associate the other cat smell with something good, and that will help ease the transition. But you'll see how it goes - trust your judgment! You know Rosie really well, so you'll have a good guide to follow.