1) Can I claim myself to be and act as a safety pilot since I don’t have a SP rating on that aircraft?
you are a “pilots assistant” only, you clearly can’t log anything, even if you fly as a safety pilot and are paid as a safety pilot, you still can’t log it unless you “take control” from him as I understand it.
2) The captain (which is not FI rated) sometime hand over the controls to me so I can feel that I am not so useless. While doing this he still remain the Captain and off course I still can’t log the time in my log book. Are we breaking any air law by doing this?
i think technically you are but I can’t imagine you would ever be prosecuted as such (unless something happens) but it’s bad practice and I would avoid it. And it’s for sure against the company SOP, as he signed for the aircraft and it’s not an instructional flight.