It seems odd to me. I can use my APs to move and then attack, but if I attack first then my turn ends and I'm not allowed to move.

Am I doing something wrong? Does this change later in the GF series?

If your AP is high enough you can do multiple attacks or spells... Although maybe i found that by a glitch where i had 32AP...

You're right. Further into the game, I found that using Haste does grant enough AP to gain extra actions per turn.