Please note that I am only licensed in New York State and this is for general information purposes only.
As the driver of the vehicle, you can be sued for negligently operation. The owner of the semi can be sued as well for negligent entrustment of the truck to you. If you do receive a lawsuit, forward the original to the insurance company which insures any of your household vehicles.
Yes, they can sue you; the better question is can they collect from you, personally. The answer is, probably not. First they have to exhaust the commercial policy available to your employer; it is, most likely, in the millions of dollars. I presume you owned a vehicle and had private auto insurance coverage on that vehicle. If you did, that insurance policy might cover you in the unlikely event that any award or settlement exceeded the insurance limits of the employer. I don't think you have much to worry about in terms of any money coming out of your pocket. For additional assurance, though, I would schedule a meeting with the attorney handling the defense of the case and have a frank conversation with him about whether you should be concerned about your personal assets. I suspect that he will put you at ease.
Please note that I am only licensed in State of Florida and this is for general information purposes only. But to answer your question, yes. You can be sued as the driver for negligent operation. The owners will be sued as well for allowing you to drive the truck in a negligent fashion.
Yes they can. I assume that your employer has already reported this accident to his insurance carrier. You should also report this collision to your own personal automobile liability insurance carrier, as you may have additional coverage under your own personal policy.
If a summons and complaint are served on you, you should immediately notify your own personal insurance carrier as well as your employer's insurance carrier.