Your flash is behaving exactly as it should. The TTL vs P-TTL question has been answered already.
By M mode, I'm assuming you mean on the flash, not the camera. I don't remember about the 360 but the 540 will adjust output from 1/1 to 1/64. With M mode, you set the flash and it simply fires a burst of light based on your settings. It does not take into any account, distance, camera setting, light metering, it only does what you tell it to do.
With the different numbers in A mode (aperture readings), again, doing exactly what it should. In A mode, the flash is paying no attention to your camera's settings. It is a Manual mode that has auto-exposure (on the flash). That is, you set the aperture on the flash and the ISO and the flash will measure the output and make it appropriate for the numbers you've set. As long as you have set (manually) the same values on the camera and flash, you will have a good exposure (pending camera shutter speed). In many situations, this actually works better than P-TTL.
All the camera is doing in A or M modes (On the flash) is firing it. It is not taking any of the settings into account.
Both (flash) A and M modes are quite useful when you are using a Manual lens (that has no A setting on the Aperture ring) because it will allow you to control the flash output independent of any camera setting.