Cartilage piercings + hair dye.?

So yeah, I'm your average rebellious punck-rocked teen but I'm good in school and stuff and have had big ambitions for later in life since I was 6 and it's not changed. However I'm really really into the whole punkrock scene and I badly want my cartilage(ear) pierced but my mum said no. I'm 14 and I've done all my "homework" on it. If I hadn't done "homework" then I wouldn't have known that getting it pierced with a gun can lead to infection and/or shattering your cartilage. So yeah, I know now to get it done with a needle. Also, it's not that expensive is it? Anyways, how can I persuade my mum to let me get it done? She let me get my earlobe's pierced first time when I was 7! And then redone when I was 9! So yearh. And my other question was, I want to dye my hair this (http://www.superdrug.com/permanent-colour/live-colour-xxl-mystic-violet-v87/invt/113638/) colour and my mum has been perfectly fine with me dying it allsorts of coulours in the past, it's just will it show up on my hair? (My hair's a really dark brown colour) Or will I need to bleach it? Sorry it's so long but thankyou!