#1) I don't understand that - we have the moral sense because it is part of our character, just as it is a part of God's character. God is perfect so He would never break it - we are imperfect so we break it. Are you saying that He can just wing it as He goes along and change things around? What would make you think that is the case?
#2) Justice, murder, rape, bestiality, greed, selfishness, hatred, lying, stealing, idolatry - how bigger can the moral decisions be?
#3) I don't agree with that whatsoever. Modern day moral standards that we made up mean nothing and neither does any other human made laws - what the laws we make up are based upon is what matters.
#4) Concerning the evidence, that's cool, you are welcome to take it or leave it - I just wanted to point out that it is at least there.
1) If morality is given by God then anything God does is morally right. Therefore if God was to command rape, murder, idolatry as morally right then we'd have no say. Also is what God commands moral because he commands it or because it's morally right?
2) His point is that if there is an objective moral law then there is only one moral answer. However there is much evidence to suggest otherwise.
3) Modern moral standards are biological. The rest of the video goes into the science behind it if you're interested. For example when a 6-10 month year old baby is shown 2 clips of a man going up a mountain. In one the man falls but is saved by another man and in the second the man pushes him off after he climbs it. Funnily enough the baby goes for the first one where the man helps the other.
4) The problem with the example you gave is that it was from a debate. The problem with that is that the debaters don't have time to give the evidence. For example, all Dr. Craig could say is that scholars believe in historicity of the NT (not quoting so might be wrong), instead of giving the examples or evidence (mostly due to the fact that it could fill a large book(S)).