Milky urine is as you say caused by excess calcium being excreted in the urine. This is as it should be with bunnies, most mammals excrete excess calcium via the feces, but bunnies do it via the urine. It’s not really a sign that sth is wrong, unless the urine is thick and pasty, like beige/gray fine wet concrete. You can adjust her diet some if you’re worried. Alfalfa and clover are high in calcium and should only be fed as occasional treats to adult bunnies. Grass is low in calcium. Here’s a short article on calcium and bunnies: http://www.rabbit.org/journal/3-5/calcium.html
There is a current thread now where our member Vanessa has listed vegs that are fine calcium-ways, you might want to check that out: https://binkybunny.com/FORUM/tabid/54/aft/140367/Default.aspx
That she’s breathing fast and shaking sounds heat-related to me. Iced water-bottles are great for that. The wet nose may be from the heat too, if she’s breathing heavily through her nose.
My Bam has a wet nose now and then, but it may of course be from dipping it into his water-bowl when he drinks.