There is a similar thread running now. The cage is her safe place. Don't try to touch her when she is in there, and most of them are a bit cage-territorial. Wait until she is out and always watch her body language carefully to see if she might be receptive. I think there is a sticky on that. Leave the cage door open and let her come out when she is ready. As you have probably read here, it takes more time for them to adjust and get comfortable than most realize. You have to build trust with her, and sticking your hands in the cage will only reinforce her belief that she can't trust you.
As for the vegetables, many of us struggle with that. Just keep offering fresh vegetables. One of these days she will surprise you and actually eat some. Timber responds best to a skewer of fresh veggies hanging in his cage. I also take greens (like kale) and thread them in his cage bars. How much he's eating I don't know, but he is doing something with them and I assume he is getting a little! Many here make chop, which is a way of kind of "hiding" the veggies. If the veggies are chopped fine, they get pieces of them whether they know it or not. Kind of like trying to trick your toddler into eating stuff that is good for him
Good luck! Other more experienced members will answer too.