Here are some ideas that may help.
1 for picking up are you bending down over top of her or getting low and turning side ways and letting her come to you.
Bending over a dog in their minds is rude and can be very scary.
Reaching out for them as well is concerning if hands have hit her before.
So try to get low even just sit on a step and have her come to you and if she comes make it worth he while by feeding some really good treats.
Also at feeding time to help her bond.. feed her her supper by hand.
You become the giver of all good things and a little less scary.
2. What about cutting her short until you and she become a team.. it a pick your battle thing.. if you can get her to trust you then you can groom. right now she not trusting anyone.
If you want to leave her long brush her at one meal.. so one food treat for one stroke of the brush. Only one meal as you want to work bonding at the other. Bonding really needs to be first.
Lad not depressed that head drop is hay brat I not looking for no fight cool her little jets and be nice.. it dog talk... only in body not words.
5 Months is not that long in a life of a little dog to get over all the hurt and bad stuff tossed at her before you got her. It going to take time.
The tough ones are the ones that teach us the most.
You live in New york and have a great many really really good dog trainers available to you what about having one come and help you get on the right track and help everyone settle in. Have a look at the dog trainers list for NY and see if anyone is close to you or you can have come.
Truly Dog Friendly » Truly Dog-Friendly Trainers
If your up to some reading try Turid rugrass book on talking terms with dogs and learn a little body language of dogs it will help all the dogs.
JL