A: Your answer depends on the type of injury your wife would be potentially claiming. For injuries that happen in the workplace, or that happen while working, then the workers compensation statute is the sole remedy for potential relief and compensation for her injuries. The workers compensation statute replaces typical remedies that would be available under the common law (for instance, a claim for negligence seeking personal injury damages). If your wife is seeking to sue for something like employment discrimination or breach of contract, then yes, she could file a lawsuit, but would want to talk to a lawyer about the facts and circumstances of what happened first.
A: Your spouse would only potentially be liable for your business debt if your spouse is a shareholder, member, or manager of the LLC. Additionally, if any of the business debt is in your spouse's name, that would also implicate her involvement in the bankruptcy proceeding.