Creating my own Fusion Drive: Do I need to buy Mountain Lion from the app store to reinstall the OS? Do I lose the iLife apps?

I just bought a Mac Mini (late 2012) with a 1TB HDD and I'm planning to install a second drive, an SSD (Samsung 840 evo) and create the Fusion Drive, and I have a couple of questions:

1- I've read lots of articles on how to do this but I'm not sure if I have to buy Mountain Lion from the app store (to reinstall the OS after I install the second drive) since I'm not able to see it on the "Purchased" list of apps, or if I can just reinstall OS X with OS X Utilities.

2- I read somewhere that if I make my own Fusion Drive when I reinstall OS X I will lose iLife, is this true? Or will I be able to redownload it from the store? I really don't want to lose iMovie, iPhoto and GarageBand and I'm confused about it.

Thanks in advance for any help and information you can give me!