1. does stress medication work?
....not sure why you would want to give her anything 
2. why is she wet around the mouth?
can you explain a little better?
3. she rubs her face on carpet and couch one way then flips and goes the other way?
...she is putting her scent on your scent
3. when is a good age to get a hair cut?
....oh I'd wait awhile on that - You can bath her yourself though
4. she doesn't like to be held, but rather stay on the floor?
...she is still scared and confussed and learning your place
5. how to train when she likes the treats more than food or she doesn't eat, how can I train her? yet she never seems hungry otherwise.
What kind of food are you feeding her?
6. is it normal for her to poop only twice a day maybe even once?
All dogs are different, when mine were young they pooped 3 to 5 times a day
7. how to train her to be held and put into pet carrier?
She is still a baby, go slowly with her
I just got her no more than 6 days ago and she is almost 4 months old. I know traing doesn't happen overnight, it takes time. I just want to get started off on the right foot and that we both are happy.