Can my employer ask me this?

Can my employer ask me detailed questions about my health, and require that I put my name on the form?

They claim the information is required so that they can get rate quotes for a new health insurance company. I've never heard of such a thing, and in the past, for any group health plan, I've only been asked age and gender.

I do not care to share my medical conditions or medications with my employer. Oddly, I'd probably mention any of it in passing conversation...but filling out a form with my name on it and listing everything seems...wrong, and likely illegal.

Someone please tell me that it really is illegal, and give me something to back it up.

Here is the list of questions.

Shoes!

My dance shoes arrived last week. They're great. Really, really great. They fit properly, and seem comfy. They have an "infinitely adjustable" buckle, but also a snap, so you can set the strap the way you want, and then get into and out of them easily. My other dance shoes have a bit of elastic to do the same thing, but I kinda like the snap.

Sadly, they are not the color I initially wanted, nor really a color I want to keep. I got them for the sole purpose of seeing if this style and size fits properly, which it does. Now I return them, and wait the time it takes to get the ones I want.

I'm happy, though.