Philz recovery is the same as twrp for example. It's no app it's a recovery that you flash from odin or you can flash it from your current recovery, if you have a recovery that is. If you don't have any custom recovery but have root access you can flash it through apps like flashify.
Every recovery can do a a factory reset, but to then be able to flash/install the rom you need a custom one.
You usually drag the rom.zip to the phones internal or external storage and flash it from there.
When you flash the rom the aroma installer will start and allow you to chose the things you want and don't want.
Hope that cleared some up. Since the i9305 is an old device there's tonnes of guides how to root and install custom recoverys. Google it.
Oh darling you just don't know how many guide I checked. They don't explain jack ****! Also, I already rooted my phone today and it didn't take even 30 seconds. I installed a bunch of apps I thought I might need such as CWM and TWRP so I can try Cyanogenmod but... I screwed up during flashing it because I messed around without checking guides and my phone is bricked. I'm sure I can un-brick it if my cable is working but my computer is not recognizing it. I'll take it to a tech tomorrow and I'll try Aroma later on.
Thanks for your reply, fam.