Not trying to be nasty, but you are seriously confused how things work.
Can I suggest to study up on some of the devices? Use the RC forums and read up on the individual components.

Here are some clarifications.
1) Your R921 is working the way it should. What you are seeing is the Quickconnect feature designed by Spectrum and incorporated by JR as well.
Quickconnect is a visual indication when the RX things it had a brownout (loss of power). The idea is: If after a flight, you have blinking RX lights, it suggests that there was a short loss of power (or voltage too low) and that you better check your onboard power system.
Now if you go and turn off the RX and turn it back on again, while the TX stayed powered up, you are simulating this conditions.
It's just a visual aid.

2) GY401
It's quite happy to run on the 5.8Vdc and you have done the correct thing by adding the step down diode cable between your gyro and the servo, as the servo is designed for lower voltage and the diode makes sure that the servo won't be harmed due to over voltage.

The gyro has 2 modes: rate (normal mode) and HH (heading hold) which Futaba call their AVCS mode.
During bootup (when you turned the RX on) the gyro works through it's initialisation (just like a Computer) and it's light will flash until it's finished with the bootup. Once done: In Rate mode the gyro LED will be OFF. In HH mode the gyro LED will be ON.
After bootup, thee gyro LED will show blinks or flashes every time you move the rudder (tail) stick. It's just another visual indication to show you what is happening.

To start with:

Keep your TX at least 1m away from your heli.
Turn on TX then RX...do NOT move the heli or touch any of the TX functions until everything has finished initialising.
Any interruption during the boot prosesses for both the RX and the gyro will make them behave oddly or malfunction until anothre reset.
These are small Computers that need to go through their boot sequence without interruptions or interference to function properly.