Can books downloaded from Google Play be re-downloaded?

If they're free, yes. But if they become paid down the road maybe not for free anymore. If they're paid, the transaction will be recorded and you won't need to pay for it again.

 

AFAIK, once something is listed as free in Google Play, it can't later be charged for. Did that change?

 

That would certainly send ebook buyers to Amazon, Barnes & Noble, Sony, etc., where daily free books that go off free a few days later can be downloaded for free after the price has risen. All transactions by those other bookstores are recorded as owned by you, including those priced for free. So the "maybe not for free anymore" speculation seems too cautious given the current ebook marketplace, unless Google wants a black eye for its ebook store.

 

They can remove the free version then reupload it again as paid. Already happened for a number of apps I have.