I see from your multiple questions some real concerns about this potential claim and your potential exposure. I think you definitely need legal counsel to help you evaluate the extent of your company's liability, if any.
As to your questions, if you have kept operation of your LLC separate from personal finances, and if you have reasonably capitalized the LLC, you should be personally insulated against the liability.
The company will be liable for work it performed, even if you personally did the work, assuming the contract, verbal or written, was between the company and the client. Unless you did something intentionally to harm the client, you should be insulated.
The fact that your home is the address of the business is not important, so long as the LLC has no interest in your home. If you are married, going forward, you might consider putting your home in your spouse's name, assuming your spouse is not involved in your business.
Admitted in OH, PA, MD, DC
In determining whether or not personal liability exposure exists for work that you performed on behalf of the LLC a close look at the facts is necessary by an attorney. You should contact an attorney regarding the threats of litigation so that he or she can advise you as to whether or not a complaint could be filed against you personally. If it is possible to resolve the threats at this early stage it may be in your best interest to explore this option with an attorney as litigation can be lengthy and expensive.