LAAT/i is Republic air transport, used to transport infantry and light armor across battlefield; it also serves in assault chopper role, somehow similar to Mi-24 "Hind". Capable of carrying complement of clone troopers into battle, and armed with heavy firepower (including missiles shown above) it promptly proved importance of air superiority in Battle of Geonosis.
Missiles produced explosions which had diameter of around 1/6th of diameter of TF Core Ship, which is shown in RotS to be 1/4th of width of TF battleship, or 792.5 meters. Therefore, we have explosions approximately 132 meters in diameter, for yield of several tons of TNT, high-end. Lasers are probably in megajoules per shot.
No other Republic air support was seen.