These aren't that hard for people who know the Bible.
First, Ezekiel 42:13 and 46:12.
42:13 - Then said he unto me, The north chambers and the south chambers, which are before the separate place, they be holy chambers, where the priests that approach unto the LORD shall eat the most holy things: there shall they lay the most holy things, and the meat offering, and the sin offering, and the trespass offering; for the place is holy.
46:12 - Now when the prince shall prepare a voluntary burnt offering or peace offerings voluntarily unto the LORD, one shall then open him the gate that looketh toward the east, and he shall prepare his burnt offering and his peace offerings, as he did on the sabbath day: then he shall go forth; and after his going forth one shall shut the gate.
The short answer is that during the millennial reign of Jesus Christ, the sacrifices outlined in the Old Testament will again be performed in the Temple that is described in Ezekiel 40-48. The nation of Israel will finally be in possession of the land that God promised to the seed of Abraham, Isaac and Jacob and will be fulfilling all the terms of their covenant with God. These sacrifices during the Millennium are also noted in Isaiah 56:6-8; Zechariah 14:16; and Jeremiah 33:15-18.
Sacrifices never took away sin. Read in Isaiah 1:
11 To what purpose is the multitude of your sacrifices unto me? saith the LORD: I am full of the burnt offerings of rams, and the fat of fed beasts; and I delight not in the blood of bullocks, or of lambs, or of he goats.
12 When ye come to appear before me, who hath required this at your hand, to tread my courts?
13 Bring no more vain oblations; incense is an abomination unto me; the new moons and sabbaths, the calling of assemblies, I cannot away with; it is iniquity, even the solemn meeting.
Sacrifices were always an object lesson about sin. Sin is offensive to God and it causes death, and that will not change during the reign of Jesus Christ on earth.
As to the prince. I'm not sure what you want me to explain. Please clarify.
Lastly, your question as to how one man can die for another's sin doesn't make any sense when you have already accepted the idea of sacrifices. Each man is under a death sentence for his own sin, but the Old Testament is full of verses about sin offerings that God commanded and accepted in lieu of death. As noted, these did not ultimately please God, or satisfy the requirements of his holiness.
Jesus substituted his own death for ours, and this did please God. Isaiah 53 prophesied of Jesus Christ's sacrifice:
10 Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand.
