You mentioned her peeing in her bedding in her open crate. does she pee in her crate when she's inside and the door is closed? How much room does she have in the crate, relative to, if she pees in the crate, will she be forced to lay right next to it, or can she get away from it by a foot or more?
Have you tried crate training?
I think she is still young enough that it's normal for her to not be getting the idea yet. You must, as i'm sure you know, use enzyme cleaner like Nature's Miracle, to eliminat the odor, get your self a blacklight to make sure all the odor causing substances are gone, perhaps get Nature's Miracle laundry detergent or treatment.
About her going pee outside next tot he paper rather than on it, i think (rightly or wrongly) I would praise her for a "good wee" for going outside.
Zack sometimes pees on the patio or on the door mat instead of in the grass or off the patio where he's supposed to, and part of me wants to interrupt him while he's peeing on the doormat (which i then have to wash off and hose off the patio) while the stronger part of me does not want to confuse him about inside/outside and as long as he's outside, i just praise him when he's done, but i'm figured out that all i have to do is stand on the door mat and he won't pee on it, he'll pee somewhere else. after abby pees next to the paper, i'd praise her and put her on the paper and pleasantly say "pee here." and do that each time.
I have not had to do what you're doing, i'm lucky to have a backyard, what you're dealing with sounds a bit more challenging. it could take her longer than expected and just having her do it on the patio rather than inside, might be easier for her to grasp than a paper. after she gets the idea of inside/outside, then start using a paper or litter box or paper? I mean, keep the paper or litter box available but focus the lesson just on inside/outside until she gets that part?
Inside, when i first got Zack, i used wee pads, and he showed a tendency to go on them, they were by the doors on the inside. It's not like he clearly got it, he woudl occasionally go right in the middle of the carpet, far from the pads, but generally, he would go to the pads. I found I had to put lots of pads, not just one, otherwise, he would put part of it on the pad and part of it on the carpet. so, i used 4 wee pads to give him a big target and that worked (this was very necessary because he had diarrhea in those days). How big of an area does your paper cover, what size is her target?
zack learned to go outside fairly quickly, i never gave him any treats for doing it, just praise, i'm forgetful and i can never remember to bring a treat with me so i'll have it at the right time. I did get a little treat pouch to clip on the belt loop, but i forget to put it on. maybe it's because i never used treats to train previous dogs so i'm just not used to it, by long habit, i just go with talking to the dog and praise and habit, repetition. It never occurred to me to teach a dog to pee on command, until i got Zack. I never had the need to do it before, and i never had the need to do it with Zack either, but i read about it and it sounded cool so i always say "go pee" when i let him outside, and then whenever he pees i say "Good pee!"
it's hard to tell if it's working because he was going anyway, but i think he might associate the word with doing it.
i think zack and my other dogs learned to go outside quickly and going inside never became an issue mainly because i always had backyards, and combined wiht my training style, that has worked well. I am sure that other training styles can help a dog learn quickly wihtout a back yard. But how quick is quick? it was just written recently on one of these threads that dogs won't really competely get it until a year old, and Zack is proof of that.
you have my sympathy! good luck!