Once you tap on the "What's New!" button on the main menu, it changes to the Collections button. It works like the Gallery, but when you've collected enough items to complete a collection you can trade them in for new rods, gizmo upgrades or reels (or even Doubloons).

The items themselves are caught around the island when you fish. They're fairly rare and some tend to be found in specific locations or are more likely to be hooked in certain locations.

Yes, normally you'd get them by reeling them in and sometimes the Old Guy In the Lighthouse will try and sell them to you. Unless you're swimming in doubloons though don't be tempted by his offers as they're not so cheap ;)

If you watch the news popup on the main menu, it'll mention the fish of the day.