No; no animal sacrifices until the Temple is rebuilt.
Sacrifices can only be given at the Temple; until it is rebuilt, no animal sacrifices.
Yes...the reason they stopped doing sacrificing elsewhere was during the reign of Josiah (roughly 600 BCE), the priests "discovered" the "long-lost" Book of Deuteronomy (, which ordered Jews to destroy any other sacrificial centers in the land and only do their rites in the Temple. Josiah followed the instructions in Deuteronomy and wiped out a number of very ancient Judean sanctuaries. Check out II Kings chapters 22 and 23 for the story.
