Nice game concept! This is very fun and I think the singleplayer mode as a lot of potential. The graphics are very top notch too as the other comments have pointed out. Gameplay wise, a minor complaint would be the controls - it would make more sense for the single player controls to be 4 vertically aligned keys (like 1qaz) instead of the arrow keys.
To sync music with game events you have two options. One, you can decide on a BPM value then build an array of "beats" at which you want the events to fire. You then store an integer representing the index of the beat you are expecting next (starts at 0). Then in an update loop, you fire an event if the audio clip (in seconds) is past the current beat (converted to seconds) you are expecting.
You can also manually set the position of objects every frame according to the music. All the math is linear so it shouldn't be too bad.
Check out our game, it is also a rhythm game ;)