Does British law let the monarch just dip into this kitty at pleasure?
That COULD be the source of mischief, yes.
Yup. Most of it is technically just family money and assets — as in personal assets. There are some restrictions regarding certain properties, but those are rounding errors. And they’re worth enough money to make Bill Gates look like a pauper. (The reason they don’t show up on the Forbes 500 is because they don’t want to. Most of the truly uber rich don’t.)