1) you can customize mp3 player, but need to edit some code, anyhow I shall add an easy option soon to edit update mp3 and video player form admin section.
2) yes, for download categories, it is using custom taxonomy
3) Yes
4) you have both option, upload or add external link, and from front-end settings, you can block any mp3 upload if you want to allow them to add external link only.
5) yes, it is compatible with mobile device
6) most are around $22-$30, and all-ons pack ( all current add-ons and upcoming add-ons ) is only $105 , http://www.wpdownloadmanager.com/download/all-ad-ons/
Sorry for the delay to reply.