You should make time to talk to an attorney. That attorney might know which of the drs that are proposed are more likely to be friendly. They will also know if the 2 percent is reasonable and if you should get anything else, like disfigurement if available there.
No. The Ins Co is obligated to advance their estimate of your disability. If it is later determined that you have more, you will get more. It is fairly unlikely that it will be a big case, but 5% might be better than 2%. There is no problem with cashing the PD checks that they send you.
We offer general concepts, but you should give ALL your facts to a licensed Attorney in your state before you RELY upon any legal advice.
This is not a situation that you should be attempting to handle on your own. The deck is stacked against you and the best chance you have of getting a fair shake is to hire an experienced workers compensation attorney.