So as an owner of a Range Rover 2005, one of the things that I have had to deal with is all of the above on the subject line.
In some cases, this type of issues will cause a battery drain and if you are not driving it for a couple of days, you will end up with a dead battery.
let me give you a run down on how you can fix some of these things. Now this may or may not work for you, but it sure did for me.
Bluetooth module. best thing to to is bypass the module. The Bluetooth technology on the module is old and newer phones will not work with it. Unplug the power and then connect the MOST system back into a loop.
what you do is get the one that has the red light beaming and connect it to the one going into the amp. Take a Bic pen. pull off the inside of one and you are left with the tube, the cover, the ink tube and the small part that is holding the ink tube. use that tube which will be put the fiber wire together. sometimes the light doesn't stay direct, so you will have to play with it and maybe eve use a straight object and then tape it together so the light passes through directly.
If the amplifier is not working. try the following. Remove it and open the inside. use rubbing alcohol and a new toothbrush to just rub the board on both sides. clean any rust or dirt you see and let it dry. it actually takes 5 minutes or less to dry. when connecting. If it got cleaned and its still working, as soon as you start connecting the wires back on, you will see the red light beaming from the amp. put the fiber plug in last so you see the red light. make sure its still on when you do. when I did it the first time, I waited to long and by that time, the radio wouldn't work.
in a nutshell, open each system and don't be afraid to clean them with rubbing alcohol. I am actually going to try to do the navigation system and Bluetooth module just to see if they work.