O man... I love my cats and my dogs and my horses... but rats... *squuueeeee!!!!* they are just so freaking SWEET!!
I work at a pet store that carries all sorts of small animals; typically, the hamsters are EVIL (though I do have to say we do get some exceptions), but the rats are always sweet, and I have never been bitten by any of the rats we have gotten. They will nibble at my fingernails a little, and they like to lick and give wisker-kisses (hehe, someone brought in some baby rats that we are trying to adopt out, and one of the little girls climbed up on my shoulder and started to groom my hair)!
They can be rather curious and love to play; I can see how her and your kitten might like each other!! :3 Any sort of foraging type inrichment will be good for her, to give her some excercise and put that intelligent little mind to work! what you might consider is getting some cardboard toilet paper rolls or paper towell rolls and poking some small holes in the side and then covering up the other ends with some newspaper. She'll likely tear it up, but it will be good fun, as the rolls will like to roll away from her as she goes to nab them. xD
Hand feeding is likely a good way to get her to warm up to you. With the young rats we have at work, I'll but some cashews or some cut up carrot bits in the palm of my hand and stick my hand in there. They'll come up, sniff around, and pick out the yummies from my palm.
Also, if you want to get her out and you are nervous about her reacting badly when you try to pick her up, you could try coaxing her into a bowl like object (we have those plastic igloos, and we can turn them upside down and they'll crawl into in, and then we'll pick it up with one hand while using the other hand to keep them from jumping out) and then taking her out that way. Once you've done that, you can go into a secluded small room where you kind find her easily and she can't really escape (like the bathroom), and sit down and put whatever you are carrying her in your lap. Then you can let her out to explore, and see if she'll climb up your body to investigate you! I've habituating a few of our less skittish little girlie rats in a similar way. You may get soiled on, but their droppings are usually pretty dry and easy to brush off, and if she urinates on your skin, just be sure to cleanse the area with soap and water, and then wash your hands real good. :3
It's so super awesome of you to take care of your friends baby like this!! Most people are so opposed to rats, that they don't even give them a chance! It's really neat that you're willing to do this! Good luck, and have fun! :3