I think there are conflicting reports on using hair dye in pregnancy. Some people say "no, absolutely not", others say "not until such-and-such trimester" and others say "not if you have an open wound on your scalp". I think it might be okay as long as you're in a well-ventilated room so the fumes don't overwhelm you.
As far as the tanning lotion, I have no idea. I would read the back of the bottle and call your doctor/midwife just to be safe.
*edited because I said "unless" instead of "if"

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