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It's not what you asked for, but right click to choose an enhanced icon. (EDIT: Oops that appears to just be a temporary emoticon)

You can put the hat on. It's in the main camp building in a bedroom. Your cursor will be wearing a hat from then on.

You can also put other clothes on, like sunglasses and shorts.

Can you don multiple items? Didn't try.

Yeah you can. You buy them with seashells.