Am I responsible for hitting and injuring another driver while driving company car during lunch break

Stop talking about this on the internet (or anywhere else). If you have driver’s insurance call your insurance co. they will get you a lawyer. If not, look into getting a lawyer. Your employer almost certainly has ins. coverage and you are almost certainly a permissive driver, which generally means you have coverage. Ask your employer who is defending you through their insurance.

If you rear ended someone in most circumstances you are libel (it is not clear to me whether your employer will be libel, the fact that you where going to lunch may or may not get them out of it) Even if you are libel, the other drivers conduct may have contributed to the accident perhaps reducing the amount of your liability. I don’t know how this will effect your relationship with your employer See a lawyer ASAP.