throughout the Old Testament, beginning in Genesis 1:26, "Then God said, 'Let Us make man in Our image, according to Our likeness; and let them rule over the fish of the sea and over the birds of the sky and over the cattle and over all the earth, and over every creeping thing that creeps on the earth.'"
God did sacrifice Himself, as represented by God the Son - Jesus. The reason is straightforward - only a sinless human could pay for the sins committed by other humans. A sinful human can only pay for his/her own sins.
As for the blood requirement, Hebrews 9:22 says, "Indeed, under the law almost everything is purified with blood, and without the shedding of blood there is no forgiveness of sins." This goes back to the OT laws (see Leviticus) that required animal blood be shed to cover sin. The animal sacrifices were a kind of placeholder until a Perfect sacrifice (the Messiah, Jesus) could make the final atonement (payment) for sins through the shedding of His own blood.
To your question on joy in Heaven while others are in Hell (and, BTW, immortal, indestructible bodies cannot be burned), the best answer I have is that those in Heaven will be perfect in every way and therefore in total agreement with God's justice. "He [God] will wipe away every tear from their eyes, and death shall be no more, neither shall there be mourning, nor crying, nor pain anymore, for the former things have passed away." Revelation 21:4
Ron Paul - Honorary Founding Father