Each attorney may do it differently, so you should have the attorney make clear how expenses are treated and what constitutes a valid expense. And yes any attorney should give you an itemized accounting when asked - that is my policy anyway.
Well, the answer is both - but I am hoping your new lawyer knows this already so I am not sure why you are asking the question here. If your new lawyer does not know what to do, I would be concerned if I were you.
I would expect you should be able to find an attorney to do this. I am a little confused - you say the personal injury case is open, but your current attorney has not filed suit? So how is there a case?
There are a good number of attorneys who will take a look at your case with a free consult and if it looks good will do this on a contingent basis. Click the contact attorney button to reach out to the attorney of your choice.
You as the client are entitled to find another attorney at any time you want. Just be aware that your previous attorney may be entitled to some payment at the end, depending on what work was actually done.