Can I sue

The next of kin or the executor of your brother's estate would need to file suit.

Can I be compensated fo my injuries?

Yes you may be compensated for your injuries. however, the larger a gap between injury and treatment will be deemed questionably by the insurance.

I was in a car accident and my car is considered totaled by the insurance company.

They can total it if they so choose. You may keep it with the salvage title. You are at their discretion.

What should I do if anything?

Sounds like a lot of nothing. No news is good news. Stop worrying.

Can I sued the city?

First, I am not sure on what basis the city is responsible for your damages/accident. Second, even if there was some connection, there is sovereign...

You are entitled to the fair market value of your vehicle. I am not familiar with this warranty from Hyundai. Is this something that was prepaid...

The insurance may take issue with you not pursuing the matter. I see no reason not to protect yourself and follow all available legal paths.

It is required that all drivers maintain insurance. You may consider addressing the issue in your custody/visitation agreement requiring proof of...

What do you think would be a fair settlement for pregnant woman car accident?

It is not possible to evaluate without even seeing the medical records. The pregnancy complicates the issues. Talk to local personal injury attorney.

Bad faith car insurance?

Your call. If you have invested this much time and energy to get it down to the $2k differential, do you need representation? The actual value...