I would like to sue sue to circumstances

I do not see the basis for a suit here, and not much in damages.

Can I hire a personal injury attorney in Billings MT where I've lived now for almost 6 yrs or do I have to hire 1 in Spokane WA?

The place of the defamation and emotional distress would be the venue for the suit but I think the statute of limitations may be a bigger issue.

Can I sue a grocery store for getting viral gastroenteritis after eating a sandwich from their deli?

Possibly - consult a local personal injury attorney.

Can a person win compensation from someone not a fault for a car accident?

You should be able to find out from your insurance company if and who it paid and how much.

Attorney Kopelson is right - best to consult with a local criminal defense attorney before anything else.

Hit and run with (possibly) no insurance and I'm the at fault driver?

I would follow Attorney Kopelson's advice.

Is it possible to have an anti gay billboard taken down?

Possibly - this is a First Amendment issue. Contact a local civil rights attorney. Need more details as to the actual language on the billborad.

Does my supervisor have the right to share my medical records with my co-workers?

No, your supervisor has no right to share your medical information with your co-employees.

What do I need to do to prove that this situation wasn't right? And something needs to be done?

Attorney Cooper posted a very insightful reply - I recommend reading it closely.

What type of lawyer would I need if my child was severely hurt in a group home needing surgery.

As the other lawyers posted, consult a personal injury attorney ASAP. There may be an issue due to the "surrendered" your child which raises a lot...