The Android version can use mods, but the iOS version cannot.
Here are the instructions for getting started on Android.
Mods you install will affect all of your saves. Many mods don't affect a save in any long-term way, though. (Major exceptions would be custom farm maps and custom crops while they're growing.)
If you want to have different mods for different saves (including none at all), you can keep different sets of mods in different folders and switch between them. It's a bit more awkward on Android than on one of the PC OSes, but it's doable.