Workers' compensation applies regardless of whether you or anyone else was negligent. In other words, how you got hurt does not effect your ability to make a claim.
Ultimately, you have to decide whether to accept a settlement. However, under Nebraska law, you are entitled to be compensated for your out-of-pocket expenses, such as medical bills, but non-pecuniary losses, such as pain and suffering, are also compensable. Accepting an amount equal to your medical bills does not compensate you for all the losses that you have suffered.
Maybe. Doctors make mistakes all the time, but that doesn't necessarily mean malpractice has occurred. Malpractice only occurs if we can get another medical professional to testify that the care that was rendered did not meet the standard of care (the minimally accepted level), and that the patient suffered damages as a direct result of the sub-standard care. If you think malpractice has occurred, contact an attorney for a consultation immediately - there may be statutes of limitation which require you to act quickly.
Yes. Under Nebraska law, if you are injured because of another's negligence, they are liable for any injury caused by the accident, including any aggrevation of a preexisting injury.