I'm not bothered by this, but it makes the haircuts pretty pointless. They gave us customisation options, but they limited somethings too much. oh well, maybe they can improve on that next time.
The main Serebii.net site says the Red Fedora is available at Lumiose Boutique on Wednesdays and Saturdays. Today is Saturday, yet they only had the Black and Grey Fedoras. If the site is wrong, then where CAN I get a Red Fedora?
You can remove accessories by taping on them again, unfortunately hats cannot be removed.
In the Trainer PR Studio, if you enter and make an immediate left turn, there is a room where you can get contacts and stuff to change eye color. IIRC, th guy says something about having to unlock different lenses, so maybe you can unlock those?