None of my girls expressed an interest in dying their hair until High School. My youngest has no interest in it at this time, she's in 8th grade but it would be fine with me if she wanted colors etc.
My oldest one did have permission to dye her own hair, but she nearly destroyed our downstairs bathroom with black dye once. It looked like she "flipped" her hair with the dye on it, and everything had black dye all over it. She was around 15 at the time, so we had to make a rule that she could dye her hair..... but not in my house. I still have permanent black dye on that ceiling and it's been more than 10 years and a new paint job... it just seeps through the paint.
My middle girl started dying her hair in late High School. She has light brown hair and went bleach blonde (for only a few days) then candy apple red, and now, when she began to look for serious jobs (she's in Grad School now) she keeps the color more muted.
It was her own choice to go with less vibrant colors so she could get a good job as a Librarian. My dh and I had nothing to do with this decision, but she was more interested in the idea of a good job opportunity than having unusual hair. I don't know if it would have made a difference, but it was up to her.
As for piercings and tattoos, our state has a law that nothing can be done in a tattoo parlor on people under 18 years of age with an ID. I wanted my youngest dd's ears pierced (she did too) and knew that professional piercers do a better job than the plastic gun at places like Claires. We couldn't get it done in a tattoo parlor, so we did go to a Mall jewelry shop. She ended up with a lot of problems with skin growing over the earring back, infections even with good care so she let them close up and will have then redone when she can have it done in a proper parlor in a tattoo and piercing shop.
Our middle dd has a number of holes in her ears, lots of cartilage piercings and an Industrial, and had them done in a tattoo and piercing parlor. None of my kids ever wanted face piercings, for which I am grateful for. Not that I have anything to do with pp who have facial piercings, I just worry about future job opportunities being compromised. I don't even know IF it would cause a problem, but she is very serious about her career and made the decision herself.
I do love the multi colored hair in the above posts. Very pretty.