Is it true that "صَلِّ" (salli) with a ياء (yāʾ) is used for the feminine, and that the correct form when supplicating is "صَلِّ" (salli) without a ياء (yāʾ)?

The statement mentioned is correct. When supplicating, it is not permissible to intentionally say "Allahumma Salli 'ala Sayyidina Muhammad" with a "yaa" at the end of "Salli" because it is unfitting for Allah Almighty. However, there is no blame upon one who says it out of ignorance or forgetfulness, due to the Prophet's (peace be upon him) saying: "Indeed, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are coerced into."