haven't seen it yet. --> correct
I haven't saw it yet. --> it's incorrect. You can say I didn't see it
difference between both (haven't seen it yet and I didn't see it) is the completion of the verb. Yet usually goes with past perfect. Therefore if you use didnt' (past simple) you can't use "yet".
other question:
eg I already have the song on my phone.
I already had the song on my phone.
(which means I downloaded the song already and it's on my phone/iPod)
They are both correct grammatically, but you probably want to say the first one if you're talking right now. I already had it is explaining an action in the past, for example if you're telling a story from the past about you having the song .