Of course, but it must do so without "Prejudice", or favoring a state, or group of states, over another. The properties in quiestion are held in trust - for the benefit of all states, not just a select few.
It may impact the ability of a resident of a state to emigrate to a territory with their chattel in tow, but the Constitution doesn't require that they be able to do that.
No, just the opposite. See Amendment V, "No person shall be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation." And Amendment IX as well, "The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people."
In other words, the federal government cannot enact legislation that deprives an individual of their property without due process and/or compensation.
And where exactly does it say that? And if it did then who decides what is prejudicial? Why would forbidding slavery, as the majority of the states did, be considered favoring those states over the minority of the states that did allow slavery? Shouldn't the territories be administered in keeping with the wishes of the majority?
No, just the opposite. See Amendment V, "No person shall be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation." And Amendment IX as well, "The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people."
Nonsense. The government was not depriving anyone of anything. If slave owner A in Alabama wishes to keep his slaves then he may, in Alabama. If he wished to move to a territory that prevented slavery then he was free to do so but without his chattle. He could leave them behind in Alabama, sell them, give them away, whatever. The government was not taking them away from him, it was not denying him of his life or liberty or his ownership in slaves. But Congress was within its power to tell him that he could not take them into a territory.