1.) Do you have a verse that says Jesus had to be both God and man to be the mediator?
2.) I can't get to your question as to why the grave could not hold him because I can't get past the fact that God can't die.
It's all over the bible, I can't think of an isolated verse that says it explicitly, though that doesn't mean there isn't one. But the bible says explicitly that He was God manifest in the flesh. So we have God and we have the flesh that He came in. The scripture says "a body thou hast prepared for me." He was both son of God and son of Man, also explicitly stated in the bible, so your argument that He couldn't have been more than one thing at the same time doesn't hold water. (Also reasoning this way, for example, a person certainly can be a fireman, say, while at the same time also being a parent, while also being a board member of a charity, and perhaps also being a student at night classes...busy life, lol.)
There were things Jesus could only be/do because He was divine, eg, to begin with, His sinlessness, as well as the scope and innumerable miracles that He performed including raising the dead, and Himself rising from the dead.......and there were things that He also had to be human in order to undertake, eg, He had to be human in order to be forerunner for humans, and in order to bear our human weakness and sins on the cross...He had to be human in order to shed His blood.
Scripture says Jesus as the second Adam was "the Lord from heaven." The second Adam, therefore a MAN, was the Lord from heaven...how much more explicit could that be? Yet we still need eyes to see it.....are you born again?