Welcome to Yorkie Talk, and congratulations on being a new Yorkie owner.
You do have a bit of a challenge in getting your little one so young, but keeping her safe and fed over the next few weeks she will catch up.
Since you are new to YT you might not have seen some of the great information in the Yorkie Talk Library section. Here is a link to the section with lots of good new puppy information.
Puppy Care and Puppy Info Library - YorkieTalk.com Forums - Yorkshire Terrier Community
Frequent feedings are so important. Her stomach is so tiny, she won't be able to hold much at a time. The moist food and milk replacement is giving her some hydration in addition to water. It sounds like you are doing ok in the feeding, so I won't go into all the extra hints & tricks that I did with my 8 week old pup (unless you ask).
Their bladders are also very tiny, and I'm not sure she is ready for crate training (just my opinion). It is however important to have them in a restricted area until they are house trained. Many people set up an Ex-pen and put the crate inside but leave the crate door open, then there is room outside the crate to walk around, eat, and potty (on training pads).
I would be very concerned about taking her outside to potty at this age, without being fully vaccinated (which could be around 16-20 weeks). You have to be especially careful not to put her down anywhere other dogs may have been; she could get Parvo which is deadly. That also goes to other places you might think of taking her like Pet Stores, and even the vets office. Keep her in a carrier in those places.
Wiping her bottom won't be necessary every time, once she has normal formed stools, and the fur on her bottom is trimmed. A washcloth or cotton ball with warm water is helpful to stimulate a bowel movement if she seems to be struggling.
Good luck, and keep asking questions and updating. We all care about your little one, and want to help you get off to a good start.