I would say
1) no, it's your responsibility to insure it as soon as it belongs to you
2) it's his fault, it's always the fault of the person who hits the vehicle in front (unless he can prove that you were driving badly and caused him to hit you) - you would be claiming off him if there had been any damage.
He must have been going pretty fast to make a mess of his vehicle.
3) You can't report it to your insurers if you didn't have any at the time of the accident... but please be aware that driving without insurance is an offence, if it gets reported to the police you could be in trouble. IMO.