When you first begin your game, combine any two monsters to create a monster with the "-ish" subtype. You may then combine an Abyss with the first monster to create a "Lobearta," a monster with high starting stats in Power, Intelligence and Defense.
If you play the game, and are on the In-Game date of your birthday (same as in the DS system settings. E.X: June, Week 2), a character will give you present, such as Cleo.
Also, on your monsters birthday, Colt will come by, and sing him/her a song.