somebody else could probably second that cause I don't have a mini 1012 at hand but yes, 2,5" SATA should do the trick.
I think it s SATA2 but any will do cause they re all compatible, no improvement should be seen with a SATA3 though but if you want to use it in a newer computer later, it should be more up to date.
concerning the transfer of win 7, if you re happy with your current installation, just make a copy of the entire disk on the new one.
if you want to reinstall, you need an installation DVD (with a usb drive) or usb stick with the installation data.
I transfered mine by cloning the disk with acronis (which is not free) but then you need a desktop to plug in the 2 hard drives.I m sure you can find something similar to acronis on google for free.
hope it helps