My little guy won't drink milk either. My pediatrician said not to worry too much. Milk is a wonderful package deal where a toddler can get a lot of vitamins and calcium in one spot, but there are other ways to get the nutrients they need if they won't drink it. Here are some suggestions of dairy products that have worked for us. My son eats cottage cheese, yogurt, cheese sticks, and yogurt frozen into a popsicle (Great for these hot summer days!) Also, you can make pudding with whole milk in it or if your little one eats soups try mixing it with milk instead of water. Creativity is a huge asset in this situation :) Also, nap and nighttime bottles/breastfeeding sessions are the hardest for babies to give up. You might try cutting out one at a time rather than taking both away at once.
As far as the waking up goes, my 13 month old still wakes up during the night some too. Try not to get frustrated as hard as that is. She will sense your frustration. If she's waking up, especially if this is a new behavior, there is a reason for it. A common reason for waking at this point is teething pain. One year molars can cause the best sleepers to struggle even if they seem ok during the daytime. If you suspect teething is an issue you might try giving her a dose of tylenol just before bed. That works wonders for my little guy. Orajel is also a blessing. A lot of babies have a hard time with separation anxiety at about a year as well. If this is the case, she just needs to know you are still there. You might try going in when she cries and either rocking for a few minutes or just standing by the crib and patting her back until she goes back to sleep. Best of luck!
You might try the NUK brand sippy cups. They have a cup with a silicone nipple that is very similar to a bottle nipple that might help with the transition to a sippy.