I also have that buzzing when turned off but still on at the socket.
I turn off at the socket at night so not a problem for me.
It's nothing you would notice. I wouldn't worry about it if the image quality is better.
2. When the unit is turned off. I.e. not standby or anything, can you guys hear a faint hissing noise coming from the back of the unit?
I'm getting this as well, though I'm also getting an electric crackle noise as well when it's been sitting in 'off' mode (but on at the mains) for a while - it's sometimes loud enough to head a few metres away.
Has me concerned it's going to burn down my house! so I'll need to give OC a call about it.
This one is a replacement I received last week after a fault in my last one.