Do you have to wet the stick before applying to the hair?

No. It's almost like a really dry lipstick. But you do not need to wet the stick or the hair. Apply to dry hair.

Is this something you have to wash out everyday? Will it get on my white pillow if I don't wash my hair that night?

I don't wash it out every night and I have never noticed any staining on my bedding. The only thing I have noticed is some color residue on my comb which happens to be white. I really am satisfied with the product for in between hair coloring.

Does this rub off on the pillow at night? Thanks!

I don't like this product. It is to creamy and doesn't dry completely. Try Tween Time Hair Color. I run it underwater and it drys completely and even gives your hair a "little" lift. I have had mine for years and couldn't find Tween Time when I ordered the other one. I just now found Tween Time on Amazon for $7.