Yes powder free gloves are best. Even the cleanest we can try to get our skin is still risky with frogs.
Pooping is a good sign!!
They are very skitish when they shed. It is a very vulnerable time for them (great video of it by the way). Sometimes it is hard to see, but they are sucking the skin from their body into the corners of their mouth and eating it.
Reds change into their hunting cloths at night when they are comfortable and will turn that shade of dark green. During the day they will attempt to match what they are sleeping on. One of my reds fell asleep next to the little blue LED light of the Ceramic Heat emitter dome one night and his back leg and shoulder turned an almost blue color to try and blend it. I have seen them stay dar during the day if they are sleeping on an especially dark leaf.
All of her actions and behavior points to her settling in. Keep doing what you are doing and she will eat for you
3" sounds like you go a female and most likely an adult (since she is at her max size). Males tend to be 2 - 2.5 inches
One other pro tip is Reds will not over eat. They will stop once they are full so feel free to put 6 - 8 crickets in the bowl for her each night and let her eat what she needs. I have noticed that if you put to many crickets in one bowl the reds wont go in to get any.... I wouldn't dive into a bowl with 20 crickets in it either lol.
Keep us updated! Beautiful frog btw!