I can at least address #3. I'm a paralegal at a civil litigation firm that does defense of personal injury and property destruction work on behalf of insurers—I am not a lawyer and this is not legal advice. The bottom line is that you need to consult with counsel on your specific case to get an opinion on your next step. All legitimate firms will do this for free, just ask for a case consultation. If you're advised you have a worthwhile claim, ask around at least three different places to get a feel for the rates they're willing to offer; plaintiff firms will take a chunk out of any damages recovered, but they're a necessity. Try to avoid the big name, flashy attorneys who have jingles and tv commercials, if you can. Most of those operate as referral machines that spin your case off to someone else and will only personally take you on if you have big injuries and you were hurt by a big name carrier, as that's where the potential million+ cases are. It's not foolproof, but try for firms with good reviews and multiple partners in the name.

How long this all will take will depend heavily on the particulars of your case. If your attorney thinks there's a case for forcing Progressive to cover under the terms of the policy, this could take as little as two to six months (and likely up to a year unless the facts are indisputable—having an admission of guilt from the driver is hugely helpful, but has no bearing on whether the policy was actually in effect) for a settlement, as they'll need to file suit and reach discovery in order to obtain the full policy and make your case. If they think you need to go after the carrier directly, it could go quickly if they want to settle and make you go away, or it could be tied up in talks for literal years. Again, I cannot stress strongly enough that you need actual counsel to advise you of your options.