what (color hair vs. hair color) do you have?

Question

My hair color is black, and the question should be what is your hair color? or what hair color do you have?. However, it turns out surprisingly to me that the question with do is: what color hair do you have?, and if I were to ask about shoe size, I had to say: what size shoe do you wear?

Now I am confused because I am not sure if I am right asking about: some abc tool's shape, a pipe's length, some xyz solution's temperature and whatnot.

Are size and color exceptions, then, what tool shape do you make? or a rule, and so: what shape tool do you make?

Answer 1

If I was asking someone about the color of their hair, I might just say:

What is your hair color?

However, if I was forced to put the question in a "What _{.................} do you have?" format, I'd probably say:

What color hair do you have?

There is an exception (and that is the wonderful thing about English – it seems there's always an exception): If I was asking someone about hair coloring; that is, if I was talking about a product used to color hair (for example, if I'm asking about something like this):

then I might ask instead:

What hair color do you have?

As for your tool question, think I would use something like:

What shape tool do you make?

although it's a rather awkward construct, and there's wiggle room for other wordings. In general, though, I think I prefer one of these formats:

What shoe size do you wear? or What size shoe do you wear?

What ice cream flavors do you sell? or What flavor ice creams do you sell?

Sometimes there are subtle nuances involved, like the way I changed flavors to flavor and ice cream to ice creams (that's because I'm expecting that the vendor will sell more than one flavor of ice cream). So, even though I could ask:

What size shoes do you wear?

I would probably not ask:

What shoe sizes do you wear?

unless I was expecting an answer like, "I wear Size 8 tennis shoes but Size 9 boots."

Answer 2

What is your hair color?

This is perfectly understandable, and I'd know what you meant. But I think it is more likely that we say instead:

What color is your hair?

Then we have your other suggestion:s

What hair color do you have?

vs.

What color hair do you have?

To me, using hair color rather than color hair implies that the person has dyed their hair, and you're asking about the product they used to dye it. What color hair do you have would make sense to me as simply asking what shade their hair currently is (no reference to dyes) but I still think What color is your hair is much more common.

For shoes, either of these are understandable:

What size shoe do you wear?

What size shoe are you?

What size are your shoes?

But I think the most common expression would be:

What's your shoe size?

I don't quite understand your tool shape comment (what would be possible answers to the question "What tool shape do you make"? Then maybe I can edit to elaborate). But the word order depends on exactly how you're asking, in any of these cases. In some cases you're asking what the color (of their) hair is, in some cases what (is their) hair color. Hair color is a single object; color of their hair is talking about their hair and then asking about the hair's color property. So it just depends on how you structure the sentence.