All sounds quite bizarre!

Could be a case of wire abrasion somewhere in the loom and the headlamp/indicator circuits are being bridged somehow? Might also be a bad headlamp earth so it's trying to earth itself through the indicators? Water in the handlebar switch gear will cause strange things to happen too. Occasionally a blown headlamp bulb can cause funny things to happen if the filament collapses in such a way as to cause a temporary short to earth or bridge between connections.

Maybe try a new bulb in the headlamp first? Next, pull off the headlamp bulb's connector (or the headlamp fuse) and see if everything works normally with the indicators. Then try the opposite by pulling the indicator fuse and see if the headlamp works normally. This way at least you'll hopefully narrow down the circuit giving trouble?

Whatever happens, you perhaps want to be checking all the wiring, connectors and switches carefully to see if there's any water ingress, abrasion and/or poor connections.

__________________