Is there a way to "own" an app so that if it becomes paid, you will already own it?
Google doesn't allow a free app to switch to paid status. So if you download a free app and they later choose to charge for it, they'd have to do so via an in-app purchase, in which case there's nothing you can do about it beyond raising a stink to the developer and Android blogs. Something else developers regularly do is make a SECOND app available on the store, this time paid, and rename the original app to indicate its lesser status, then either stop updating it permanently, or turn it into a trial version. Either way, you'd be SOL in this scenario.

Also, I don't believe they have any sales that reduce app prices to zero on the Play Store (someone can gladly correct me if I'm wrong), unlike Amazon. There was one year they put a ton of apps on sale for $.10, but that's the lowest price I've ever seen a paid app discounted to. That said, if they did put it on sale for nothing, you would go through the purchase process and see the full price, along with a discount of the same price, which means it would still count as a purchase on your account. The same way they do regularly with movies and music. Those have all gone back up to full price, but I still own them.