Can women chant at Mass?

 
The short answers are:

In the Extraordinary Form, yes (no surprise there), but they are not to form part of a choir of clerics (a "clerical choir") situated in the sanctuary (inside the altar rails).  So, the choir should be placed outside of the sanctuary (and, typically being composed of men and women and usually often do not wear any particular vestments or robes).  The Church's norms from early in the 20th century that suggested the answer was "no", were actually saying "yes, provided..." (as above). 

In the Ordinary Form, the same answers should apply.

Grab a look at Jeffrey Tucker's recent article getting to the bottom of this here

How to do the Offertory Chants?

This is one way: the more complicated, but authentic.

This exceedingly rare book appeared in 1935 to provide the complete offertory verses for the Offertory chant in the Roman Rite of Mass.

Note that these are not Psalm tones but thoroughly composed chants that add a beautiful dimension to the chant at this point in Mass.

It is a much-valued addition to the CMAA's liturgical library, applicable to the Ordinary and Extraordinary forms.

Buy it here and/or download it for free from here [http://musicasacra.com/books/offertoriale1935.pdf]