That is completely correct. However, there is one thing about the trap medal. Sometimes, it's more of a curse than a boon. The traps are set in a random fashion and may sometimes hinder your strategy plans for the battle. That is something I don't enjoy
As for the names, they may undergo a certain change, I don't know
If they do, I'll fix it promptly as soon as I get the english version of the game from my friend.