What is happening here is that the insurance company is trying to protect themselves more than they are trying the protect you, and the lawyer is the lawyer for the insurance company. That is why in cases where the insured person does not have enough insurance it is vital that they retain their own lawyer to look after their interests.
The lawyer for the insurance company should have told you this.
A) Yes, you are most assuredly entitled to have copies of any documents that you signed, and you should have been provided them already.
B) You can request them, but it will be up to you to pay for the copies. You would request them from the reporter.
C) Yes. No party is required to cross examine another party, and if that lawyer does not find that there is any merit to doing this the lawyer can decline to do so.
D) Yes. You most assuredly have to be present as if the insurance company wants to settle for over the amount that you are covered you would be stuck paying the money. At the same time, if you are there and it is clear that you will never be stuck with owing any money then you don't have to participate much in the mediations.
E) Yes, you have the be informed and that is my point. This is the area that is of most concern based on your facts.
I believe there is no question F
G) You should immediately consult with your own lawyer face to face and that lawyer will let you know how that lawyer should become involved going forward.
Have I answered all of your questions?