Yes!
This is actually a good point for Catholics to use. Thanks.
Yes. :)
This may be a bit esoteric for someone not already thinking in a Marian mindset, but (Genesis 3:15): "I will put enmities between thee and the woman, and thy seed and her seed; she shall crush thy head, and thou shalt lie in wait for her heel." Granted, there's dispute about the "she" there--some translators feel that the Latin Vulgate is incorrect on this point, but either way, there's some notion about the woman being part of the battle.
I don't think you'd argue that what made the Ark so effective in battle was its contents, not the Ark itself. The Ark was only the vessel through which the power of God flowed.