Poor Amphibian vs Amphibian vs Hanging Out with Water Mage

[tinkthank]

Being a poor amphibian means that when you are underwater, you suffer movement, attack, defense, and encumbrance penalties. Ok.

Reading the little blurb on "amphibian", one can see that the unit in question "does not suffer movement reductions while fighting under water" (quote from in-game pop-up). Does that mean that they do, however, suffer from attack, defense, and encumbrance penalties? My guess is "no", since these are not listed under their stats as being reduced when underwater, but I can't prove it. Anyhow, the text confuses me. But this brings me to my next question.

When a normal unit goes underwater under supervision of a water mage, does it suffer any penalties? What about an amulet of breathing / bag of air / etc?

When an aquatic unit receives an Amulet of the Fish (I hope that is the item that lets it breathe on land), I dont see it suffering any penalties -- right?

Well thanks in advance.