The Latin to the Greek sometimes leads to difficulties in translation, but in this case it doesn’t matter because the soul is spirit, not flesh.
The Holy Spirit is neither man or woman. Good question...
You are essentially correct. The Latin word for soul, anima, is feminine. This is similar to the popular practice of calling the personification of Wisdom in the Old Testament "Lady Wisdom" (see Proverbs 9) since the Greek word for wisdom, sophia, is also feminine.