Can a company withdraw a workers compensation settlement after it is offered and accepted by me?

Ask your attorney. I don't think you have an agreement until is signed and approved.

Why am I being offered $1000 "compromise" on my bodily injury claim to "close it"?

Yes they want to close the claim. They don't want to pay for administration of the claim and are afraid that you might be more hurt than you realize.

Who's fault is it? Can there be a court date?

Let your insurance handle this. It sounds like the conditions were bad. Thankfully it seems nobody got hurt.

What do I need to do to make her pay for this

Dall a personal injury attorney as soon as you can. Do not attempt this on your own.

How can I go about a lawsuit?

You can get your records and have them evaluated but assuming this gets straightened out there is probably no med mal case.

No Bodily Injury Coverage / Personal Injury Claim / Vicarious Liability?

Give it to your insurance company and let them sort it out. I would not worry too much about this.

Is this medical malpractice?

Doesn't sound like malpractice to me. A change in opinion based on new information sounds like good practice.

Is there anything I can do for them missing my blood clot? That seems like a serious oversight.

Fortunately they seem to have this under control. I don't see a case here.

Do I need to talk to the detective?

No you don't have to cooperate but unless you have some good reason not to cooperate I would.

Sounds like a case to me. Contact a personal injury attorney.