Hey look, he found a new mythril spear.
Jump is as it has been in previous games, removing the character from the fight for a little while and letting them attack upon their return. If the character is equipped with a spear, the landing attack does double damage -- that's not a documented feature, but c'mon, you should know this already. Edgar and Mog are the only two characters who equip spears normally, and Edgar generally has better things to do, so Mog's the go-to dragoon for the game.
Mog is a Geomancer... sort of. His special skill is Dance, but doesn't get any of the abilities Dancers got in Final Fantasy 5, so
. He has eight dances to learn, each one associated with a kind of terrain. When he's Dancing, the player loses control of Mog, and Mog automatically uses one of four attacks each turn. Which set of four attacks depends on the dance, of course.
The rare attack for each dance is an animal of some sort, so I guess technically Mog is also a Trainer with !Animals... sort of.
Mog already knows Twlight Requiem from the beginning of the game, when he fought in a cave. The attacks for Twilight Requiem are Cave In (reduce target's HP to 25% and Sap it), Snare (kills an enemy and disallows final attacks), Will o' the Wisp (fire damage to one target), and Poisonous Frog (inflicts poison damage and poison status ailment).
Plains areas teach Wind Rhapsody. That moveset is Wind Slash (wind damage to all targets), Sunbath (HP restore to all allies), Plasma (lightning-elemental to one target), and Cockatrice (HP damage and petrify).
Forest areas teach Forest Nocturne. That moveset is Leaf Swirl (damage to all enemies), Forest Healing (removes status ailments), Will o' the Wisp, and Wombat (HP damage to one target).
Sandy areas teach Desert Lullaby. That moveset is Sandstorm (wind damage to all enemies), Antlion (kills a target), Wind Slash, and Meerkat (Hastega).
Mountain paths teach Earth Blues. That moveset is Rock Slide (HP damage), Sonic Boom (HP damage and Sap), Sunbath, and Boar Brigade (HP damage, ignores defense).
Aquatic areas -- the Lethe River and the Serpent Trench -- teach the Water Harmony. That moveset
includes El Nino (water damage to all foes), Plasma, Apparition (confuse a target), and Raccoon (healing of HP damage and status ailments).
Urban or indoor areas teaches the Love Serenade. That moveset is Will o' the Wisp, Apparition, Snare, and Tapir (removes status ailments).
The last dance, unobtainable for now, is the Snowman Rondo learned from icy areas. That one allows use of Snowball (half target's HP), Avalanche (ice-elemental vs. all enemies), Snare, and Arctic Hare (HP restore).