I can only respond with #1, but the at-fault driver's insurance won't pay anything until you settle a claim. So patiently waiting may instead get you sent to collections.
In most jurisdictions (I suggest you verify) you have 2 years to finalize a claim. You are on the hook for all bills until that time; anything your insurance pays they will want to recuperate through the claim you settle- you have to pay them back. If you use a lawyer to settle your claim, many insurance companies allow subrogation (so they pay a % of what you owe them to a lawyer) but not all do (so even though you have to pay back the insurance company you owe the lawyer a % of your share based on the total amount.)
Unless you are seriously, dramatically and life-alteringly injured, don't expect much by way of a pain and suffering payment. Both my husband and I have life long injuries due to car accidents, but they (at least right now) are more annoying than life altering; our settlements paid our current medical bills but will do very little going forward; the pain and suffering payment as well as the "future medical" payments were laughable, and that was with the assistance of a lawyer. We are quite concerned about changes to insurance making these pre-existing conditions that will prevent us from getting insurance later on...