If I go to court for my auto accident claim and I lose, do I have to pay their costs?
Court costs should be of little worry in the grand scheme of your claim. The majority of claims never go to trial. In addition, a good lawyer is not going to put you in a position with paying costs under any circumstances. It is possible in some circumstances to pay costs if an offer of judgment is made, i.e. you refuse it and a verdict is for that amount or less.
There are no formulas to determine damages in a personal injury case. What's fair is based on what one could expect a reasonable jury would award and then factor in the costs and risks of suit. You need to move in a position of strength. That's only going to come by appearing that you know for certain what is fair and prepared to back up your demands if they treat you unfairly. Realistically, that means having a good trial lawyer, not just a lawyer who says they do personal injury work.
Take advantage of the opportunity to talk with the best local lawyer. You are under no obligation to hire the lawyer; you'll get some helpful information and make informed decisions on how to proceed.