Did women work in the Old Testament temples or in the Book of Mormon temples? Were baptism or endowments done in these temples?
There is much we don’t know about these ancient temples, but there are answers we can extrapolate from what we do know. First, we know that work for the dead could not be performed in the temple until Christ bridged the gulf between the righteous and wicked in the Spirit World. We can read more about this in Doctrine and Covenants 138:29-32:
The work in early temples appears to have revolved about sacrifices (which symbolized the sacrifice that Christ would later make for mankind.) Interestingly, they did have large fonts of water held on the back of sculptures of oxen, as our baptismal fonts do today (1 Kings 7: 23-26). However these were for the Priests to be ritually washed. Sacrificial animals needed washing as well. Laver – Bible Dictionary
They did have a form of initiators for priests as evidenced in Exodus 40:12-15 with the washing, anointing, and clothing ceremony.
Some apocryphal gospels, such as The Protovangelion of James (also called The Infancy Gospel of James) have Mary living in the temple and sewing the veil, and I recall that there may have been female Levites assigned to the choir, but I don’t think these things were done in the temple proper.