Map animation. You don't get to see anything. Now, Roxas would be right, except that's if he uses a sword after being given Anima abilities. You were talking about using Anima with Anima abilities, which indeed would be "map animation".
Nope. Map animation.
Guess again. Map animation.
Correct. Ranged animation without the spell. Raises his sword, then lowers it; no damage is visibly dealt but it will be incurred post-battle (though actually, all damage is calculated before the animations are even played in all cases anyway; I mean you won't see the effect until after the battle).
No problem.
tl;dr: Try it yourself. Any question you can answer on your own should be.
Edit: Know about the Stone glitch in FE 8? Just think of what happens when you give Eirika an A in dark magic. That right there would have answered all your questions.