RE: Heli assembly
Ok first of all it looks like you have everything you need. but before I go any further did the gyro realy come installed that way? seems wierd to me.
charge your battery
If you look on page 22 of your manual you'll see where each item should be connected to on the receiver, this is for futaba/hitec radios so it should work on yours. once you have the esc, servos and gyro plugged into the correct ports of the receiver. don't connect the motor at this point but connect the battery to the esc and check to make sure all the servos are doing what they should, if they are opposite then go into your heli radio and change that function to "reverse". once you've done that you can start leveling the swashplate and programming your throttle and pitch curves.
I suggest that you get together with someone locally who has your radio and get him to help you program it. there is a lot involved.
forgot to mention, you don't need a separate battery for the receiver, the esc should have an integrated bec (battery elimination circuit) which reduces the voltage from 11.1v to 4.8v for the receiver).