Why does Giran pop up randomly after almost every mob I fight then drop an item that increases my zeni? One time a giant fish popped up... I'm confused, it's always at the worst times too.

Those are event mobs which drop event coins after you defeat them. You are able to use the event coins to draw out of the event wagu machine (5 coins = 1 draw)

so don't use them? they disappear when I right click them.

When you right click them they don't disappear but instead they appear in the event wagu machine event coin inventory.

On the bottom right corner of your screen click here:




Then you should see the amount of coins your have here (look in the red circle):