I assumed you had an aftermarket alarm, I don't have it on mine as 2WD so don't know about the Ford alarm but defo if you opened a door with it armed the alarm would sound as it would simulate a break in.

The bootlight is independant of the interior lighting and if there were a problem with it, it would not make the interior lights stay on.

To stop the drain you need to temporarily remove the fuse although this will also stop the central locking from working and the electric mirrors.

Basically the earth from the lights has shorted to earth someone, it could be a faulty door switch I.E jammed closed (So the switch is in the open position) I would disconnect each switch one by one and see if the light extinguishes.

Yes the tall relay has a timer built in, this relay is for the courtesy delay side.

Martin