Frau can be Woman or wife. But it's pretty much always woman if it's just an article in front and wife if it's a possessive. But yes The hover translations are just a guideline you can't solely go off of them
Strictly speaking, you have a lot of 'stuff (eg sugar)' but you have many children; If it's countable then it's many / If it's measurable (by weight or volume) it's much or a lot.