How did you come to adopt her? Didn't she show any of this behavoir or didn't the people from whom you adopted her tell you about her? She sounds like she has some trust issues with other people. If you're sure you want to take her on and not re-home her, I'll suggest a few things that might help but mostly what will have to happen is that she is given lots of time to come around in her own time.
What you need to do is convince her that you are GREAT....that all the things she likes and needs come through you. That means hand feeding her for a while. Stand across the room and if she makes one step toward you, toss her a piece of food. Don't lure her with it but instead wait for her to take a step first, then another step the next time and so on. As she comes to realize that by coming over near you gets her food, you can start a little more training. Stand there and wait. See if she'll sit on her own. When/if she does, tell her, "yessssss!" gently and give her a treat. In other words, try to see if you can get her to do a very few little things to earn her kibble and/or treats.
When she jumps up and acts all crazy, turn your back and ignore her. Don't look at or speak to her. Wait for a second or two of calm, quiet behavior and then drop a tiny tid bit of chicken or other meat on the floor near you. Be sure and don't reinforce behavior you don't want to see repeated.
As for the leash, I'd skip the outside walks for now unless you have a fenced yard. There or in the house, you can practice getting her to like to come along with you. (no leash...just on her own for now. Later we'll work on getting to like the leash) Again, like before, if she comes just a few steps near you, reinforce with a high value treat or anything she really, really loves. Find out what she loves and use it as reward to increase behavior you like. Be cheerful and quiet, calm and non intrusive. Give her her space but reward her for closing up the distance between you and her and for relative calmness.
This will likely take time. Don't be pushy with trying to pat her and stuff. Let her come to you when she is ready. She should adapt after a bit. Remember to control the things she likes and needs. Wait for a second or two of a behavior you like; (ie: calmness, no jumping up, sitting perhaps, coming closer to you in a friendly, quiet way, following you etc) and reinforce those types of behaviors with part of her meal, a higher value treat, a favorite toy. Save all the good stuff for reward and don't give her the things she likes when she is behaving in a way you don't like. In other words, don't by mistake reward lousy, ornery, shy, fearful or obnoxious behavior.
There are other things you can do too as time goes on, but for now, I'd work on getting her to trust you, giving her more time to adjust and just hang out near you. Work on being calm yourself, not gushing over her, paying inordinate amounts of attention to her unless her behavior is calm and nice. Just be there by her without pushing yourself on her...kind of like you're both sharing a residence but that's about it...be kind of a cool customer if you know what I mean. That will give her time to assess things and work things out. Are you living with other people in the house? Or is it just you? Be sure other people, even visitors give her space and don't encroach on her. Just give her time.