Is the event chest (the one which you open with silver coins) is guaranteed to give only event girl cards? Because I opened it twice and both times got non-event girls - is that a bug?
No. It is standard to get girls you already have in your collection, and it is not confined to the event girls. The point of the event chests is to give you a huge amount of girl cards so you can do a bunch of upgrades. I would save up your silver so you can do a ten-times pull toward the end of the event.