There's this game on the App Store called Flying Hamster HD, before it used to cost like $6 or something now it's free. My question is what happens if I do get it while it's free? When the price comes back do I have to pay for it? And what if I delete the game when it's free and decide to re-download it after it becomes paid?
When it's available for free and you buy it you get it for free. It's impossible to charge you afterwards because when you decide to download it because it's free.
Many apps become free over time, and that's one of the ways how I save a lot of money.
So in short, free = free (watch out for in-app purchases though, they are never free!)
To give you a better detail about updating apps: