1. Linux Mint uses Ubuntu`s kernel, so build instructions are compatible.
2. The only patch needed if you use Realtek 8723 PCIe wifi adapter. There is no proper support for it in mainline kernel yet. We will publish the patch on our wiki shortly.
3. Before recompiling try to upgrade or make fresh install of new Linux Mint 13 MATE http://www.linuxmint.com/edition.php?id=104