Should I take the settlement offer

You don't tell me what the policy limit is of the other party. But without being in Texas I'd say that your attorney would know best.

Hey good for you, hit and run. You better hope no one got your tag. Go back the contact the owner and report to the police. If you have insurance...

I am still having problems with auto insurance refusing to cover my accident. I wrote in a few months ago and want to follow up

You need to use Google or Avvo to find a local attorney.

Do I have a claim?

I also agree with attorney Owens. But I add that the "repair" could be negligence. In my state if the affected area is larger than a given amount...

Can I do something so that it will reduce the payment for the following situation ?

You're young and have a long time to pay this off. You should try to negotiate both the amounts and a payment plan. Do you have an auto policy? If...

Does business insurance generally cover expenses associated with representing a lawsuit?

You need to read your policy and ask your defense attorney.

Taxi, passenger and a driver case

Basically yes, but I or any attorney would have to see the release and other documents to give a good answer.

Do I need to get an attorney, or is there something else I can do?

First the insurer will write a "supplement" on the "hidden" damages as the shop repairs. Second they owe you a rent a car of similar size.

Do I have to sign over my car?

Because the insurance company is buying it. It's a total loss and the title needs to be turned in to DMV.

How can I submit a written appearance by the end of today?

Follow attorney's Schall's excellent advice. He's put you on track of the company and they do owe you a defense.