I've dealt with many, many abandoned and abused animals, from ferrets to horses. Almost all have had complete turn arounds over time. One or two had been so abused for so long that they never quite forgot it, but they did learn to trust us and to relax, just certain stimuli would still make them react (although usually MUCH less so.)
As far as her crouching when being picked up, it helps to put yourself in her position. How would you feel about some giant swooping down and quickly bringing you up to her eye level, with your feet so far away from ground! Especially if in the past the giant might have dropped you or even thrown you? I know YOU haven't done that, but her previous owners may have.
Try spending a lot of time down on her level. Sit on the flor and let her climb into your lap, lay down where you are lower than she is and let her climb on top of you, like up on your chest. Do this a few times a day without picking her up afterwards. (Helps if the whole family takes a few turns daily.) Also, for a few weeks, try to *always* get down on her level before picking her up. Squat down very low a few feet away and let *her* come to *you* instead of leaning down over her and scooping her up.
As far as the newspaper, if she has a naturally nervous or high strung personality, she may never get over being "spanked" with a paper when a pup, but you can help her be much calmer and less fearful. It takes time and concentration for the really high strung ones, but the following has always worked for me, whether it was a newspaper or magazine or broom or flyswatter (seemingly some of the most common "phobias" I've encountered in abused animals.)
First, every time you go to pick up the item, like the newspaper, love her first, tell her in the 'good girl' voice how wonderful she is, then slowly sit down and tell her you are going to read the paper and she is just such a good girl to let you read. Do this a few days or so of this, being very careful to rattle the paper as little as possible at first, but slowly getting more "usual" with the rustle and rattle as the days progress.
Sometimes this alone works, if it doesn't, after a week or so try _very_ slowly introducing her to the newspaper. First, just the normal rattle of reading it for a few days, later place a single page down on the floor and completely ignore it. When she finally goes to check it out, completely ignore that too. Leave it there (which can be hard if you're used to a clean house! lol) Once she's checked it out and seems ok with it, the next day, leave a whole paper on the floor or in her toy basket and repeat. Just completely ignore the newspaper and whatever she does with it. (If she pees on it, of course pick it up! lol) Let her learn that *you* and the newspaper are NOT always associated. Of course, NEVER wave the paper at her for any reason!
If she *still* cowers from the sound, try opening the newspaper on the floor, leaving it a few minutes, then a few feet away (like around the side of the couch or something) lie down and let her come up and love on you. Start playing with her, something energetic which maybe your other dog can join in on and let it "accidently" carry over onto the paper. Do this a few times, letting the paper get mangled in the process (hope you've read it first! lol) This last step has worked for me on even the most high strung pets (except for one, a truly sad case of longterm severe abuse.)
If she's relatively calm and not high strung, just "reading" the paper on the floor and letting her walk and play all over it may be enough.
Mostly, you should see a lot of her old fears fade with just Time and LOVE. She's a lucky girl to have found you!