When you get your ESCs they will have a built in power supply to power your flight controller called a BEC (battery eliminator circuit). This will supply the 5v that your FC needs. There will be a triple wire coming off your ESCs. It will have a red, a black, and probably white or yellow usually hooked together in a strip of wires (a connected bunch of three) The red wire is your +5v, the black is ground, and the white or yellow is signal that hooks up to your FC in the motor pins. Even though every ESC will have this, only use ONE of the +5v wires to power your FC. Just hook up the signal wires on the other three. Quanum is a HobbyKing name that they use on stuff that they make or have made for them. I have their Quanum FPV headset. It is something that they actually have made just for them to sell exclusively. I searched for that TX and it only shows up at HK. Yes throttle gives it power to fly. Look at that diagram that Bartman gave you and remember the mode 2 gimbal set movements. It's stuff you need to learn. After looking more closely at the APM FC I see you will be hooking up your ESCs in the OUTPUTS section. I don't see a dedicated power in port but there might be one. If it has a place to plug in just a +5 and a ground, do that following APM's instructions and not mine.
Also, it looks like that Quanum TX is designed to work specifically with your APM FC and with multirotors in mind. From the switches it has on it I don't see how that is possible but that is just my opinion. I use a different FC and TX.