I add links to post whenever I notice a useful resource on the forum.
http://quadcopterforum.com/threads/lipo-guide-or-information-nexus-choosing-care-repairs-disposal-and-more.4699/
S comes from what is called a cell configuration.
3S1P means 3 batteries in Series (double voltage) and 1 in parallel. Turnigy sells their 5200 multistar in 3S2P and 3S1P, the difference is that one has 6 smaller cells and is a lot thicker and the other only has 3 5200mAh cells
Well most quadcopters will do high altitudes, if you just upgrade the transmitter to be longer range. Just get a RTF that is within your budget (I suggest getting a Phantom 1 because of the longer flight times) and get a transmitter like a Turnigy 9XR with a 1000mW 433mHz module you could...
Make sure the motors were on a level plain when calibrated. If the landing gear are off a little you can have the motor shafts against the bottom of a table. Probably jsut was not level when calibrated.
Go into your receiver test and make sure everything is at 0, if not trim it to 0. You also might want to learn how to fly in just stabilization mode, it is not much (if any) harder to learn than in auto-level mode and you'll be able to fly better.
What transmitter/reciever d oyou have? Is it PPM, or PWM? and regarding the red wires; it does not really matter, if it gives you problems you can unplug them, I leave mine in the cable, as I don't want to worry about something causing it to short if the wire gets out of the tape or...
http://quadcopterforum.com/forums/first-build.10/
Click the create new thread button, this will make it easier for me and others to help you with the project's future problems.