Can i seek any compensation from the at faults party insurance, and if so what kind?

Consult a personal injury attorney as soon as possible. Use the finder if you need help.

What can I expect and how long can I wait before filing as I would like to see if the lungs correct themselves first.

More information is needed but best to consult a personal injury attorney as soon as possible.

How can I sue that corporation i used to work for, now that I quit. and how do i get health insurance for it

You can consult an attorney for a review of your facts.

Can sue for defective. Surgical. Implant

Yes in theory but more information is needed to evaluate.

Is it inappropriate of me to write a letter to the veterinarian? I would like to ask for some of my payment returned.

You can always ask but I doubt the Vet will agree.

Can I still sue the hospital for birth injuries?

Consult with a Texas med mal attorney as soon as possible.

What rights/options do I have? Fmla leave? Worker's comp? Will filing for WC make my employer upset?

Consult a workers compensation attorney as soon as possible.

What legal action can I take and if none, can I slander her?

I doubt the damages would justify the expense but feel free to consult an attorney.

Is a Medical Malpractice attorney sufficient or do i need a Dental. And is it better to contact the attorney by phone or email

Use the finder and make some calls. Any malpractice attorney can look at it but if they have some experience with dental it might help.

If your vehicle had prior damage it is relevant to the calculation. They can get that information from reports or observation.