A 1--So far, it sounds like the other driver's company is doing OK by you; you shouldn't need to hire an attorney, who will get up to 1/3 of what he/she gets for you. Give them time.
A 2--If you've lost any work because of the injuries, give the company a fair estimate of that loss and see what they say. Also, travel (taxi, ambulance, mileage) to and from medical visits is fair. They might even offer something for pain and suffering, but don't try to get rich on that.
Be sure all the bills are in before you agree to a final settlement; sometimes they take a while to arrive. (One asker here said a bill took 1 1/2 years to show up!)
If the other driver doesn't have high enough limits on their insurance to cover all your bills/damages, you can claim the difference under your own policy's Underinsured Motorist coverage, which I hope you have. Then your company can (try to) collect; it has experience and resources that you don't have, and that's part of what you pay for. Ask your agent or adjuster if that becomes necessary.