she explains how she made the headphones here http://offtherailscakes.co.uk/beats-by-dr-dre-headphones-cake/
Personally, I find a good clear picture of details is far better than a tutorial though, doing such a complicated cake should mean you have the skills to replicate. I would just google image 'cake headphones'.
They make edible markers in just about every colour, yes there are white ones. You can also use a script brush and paint with white colouring.
I'm afraid I disagree about the grooves, I would be pretty disappointed to get a record with no grooves, that's a pretty important part!
I have an adjustable mousse ring, starts out at 12" and can be adjusted down to 6", just lightly imprint, tighten it up, imprint again, etc. You can use larger circle cutters to finish it off.
I'm sure there are easier ways if you google it, that's just what sprung to mind.
It looks something like this http://www.aliexpress.com/item/FREE-shipping-stainless-steel-size-adjustable-circle-mousse-ring-retractable-cake-mould-mold-baking-tool-set/917767325.html
I remember reading on here ages ago about a girl using a frying pan to make the imprint.