What a lucky little dog
I would concentrate on her general behaviour in all situations which will help with all the individual issues below.
So she needs to learn calm, she needs to de stress and if you can be the source of this rather than chasing after rabbits brilliant!
I would use a clicker and just start by click and then giving a treat do this loads of times a day - give her whole meal by this method for several days.
In the meantime keep her on a long lead and do not give her the chance to bog off after little furries!
Once she knows that click means treat you can click her when she is calm. So if she is lying down quietly after a walk click and treat her - make sure you are near her so she can have the treat in a calm lying down position.
Do this for several days calm = treat you could have a word - I use chill guys! If I say it to my lot they all go somewhere comfy and lie down or on a walk just stop chasing and gather around me. It will take time to get to this stage but by clicking an emotion your dog will soon respond by giving you the emotion in return.
- barking in a really loud/shrill/panicky way at certain visitors.
Meet the visitors outside if possible but does not really matter when the dog barks take him out into another room ask him to chill and when he is calm return him back to the room if he barks remove him etc. Is there a specific thing about these visitors that sets him off, what they wear, are they loud, a certain sex etc?
If he is calm let him stay in the room and get the visitors to drop treats on the floor but they must not look at the dog. Very very quickly the dog will learn calm = treats = visitors = treats (you will be back here asking how to make him leave people alone!)
- jumping up Just turn your back on him. Everyone must do this even the people that say I don't mind! Make every one do this and only strike him if all four feet are on the ground.
- nipping at hands if holding a toy/stick/bit of food. Really worried about her doing that to a child.
At this stage do not hold toys, sticks etc if possible if he is around. You need more general control of him. So if you are holding food send him to his bed treat him in his bed rather than let him pester you. Again if children are around with toys he can be having a chill out session somewhere else.
As he generally calms down you will be able to ask him to sit or down and then give him his own toy or treat and he will again realise four feet on the ground = his toy.
- running off after rabbits etc. Have had to put her back to walking on the lead which is sad as she loves to run.
I would walk on lead for a bit - he is just doing what terriers love best! However it can endanger his life if he chases with no control from you. I would leave this for a bit and concentrate on the above for a month and then revisit this. But in the meantime get him a toy he loves a furry tuggy toy is usually great for terriers tie it to a bit of string and let him chase it with you in the garden. Get someone to hold him and you run away and so when he is straining to get to you call his name and run and he will chase the toy.
So not leave the toy lying around he can only have it if he chased you for it and then it is put away. This will become the special toy!