I'm not an adjuster so I'm not able to tell you who is at fault. With that being said, most of the time, the person who initially caused the accident would be responsible for the damage to both vehicles.
It's impossible for me to answer this question simply because I don't know the specifics of the accident. Furthermore, the only people that can determine fault are the specific claims adjusters assigned to this claim.
Unfortunately, fault can only be determined by the claims adjuster assigned to the accident. However, for the other part of your question, because you were driving your company's vehicle on company time, if you were to be found at fault then the company's insurance would take cover the damages.
You can't really get no-fault unless you live in a state where it is required. Currently, 12 states have no-fault insurance laws: Florida, Hawaii, Kansas, Kentucky, Massachusetts, Michigan, Minnesota, New Jersey, New York, North Dakota, Pennsylvania and Utah.