What are the connotations of "u'Farsu ha'Simlah"?
Rashi and Ramban #1 (citing the Sifri and the Mechilta): It means that they clarify the matter (via the two pairs of witneses - Sifri) like a new garment. 1
Why does the Torah write "Velakchu ... es ha'Ish" and not "Velakchu oso"?
Sifri: To preclude a Katan, from the Din of Motzi-Shem-Ra. 1
It is not clear however, as to why this D'rashah is necessary. See Torah Temimah, note 143 and ha'Torah ve'ha'Mitzvah, Siman 93.
Since it is the father who speaks ("es Biti Nasati ... "), why does the mother also spread out the garment?
Ramban: Because it is generally the women who deal with the cloth and who are more expert in matters concerning the blood.