Battle Theme - Sounds pretty good. Obviously old-school-FF inspired, but it lacks a bit compared to those songs. It gets to be too repetitive, and there's really not enough going on with the music to keep interest. It might get annoying to have to continue listening to that over and over. Also, watch a few of your harmonies, they sound offkey.
Lydian 47 - This one was great. I couldn't find as much wrong with it as I did with the first one, but it's still very bland at this stage. I would suggest filling out the sound a bit, maybe add some quiet strings or pads in the background or something.
Bar 44 - They seem to get better and better as I listen to the next one. The only thing wrong with this is the snare you used. It's too powerful for the song, and you should use the electric snare instead of the acoustic one.
World Map 67 -
This was beautiful. A bit predictable, and I don't agree with the bottle blow instrument and the jingle bells, but nevertheless you write very pretty stuff.
Anyway, that's my two cents. Take it or leave it