#1 Does the green light go out when the batteries are fully charged, as described?
Yes, I think so, I remember green showing when you plug it in to the charger, but having used them for a while, I decided to experiment with normal batteries, and of course, it works great - and it lasts longer than charging the included 'charging batteries' - no problem with picking up the signal either using the normal batteries.
#2 Can it connect directly to the optical audio on the TV, does it come with the cable for it?
No is the answer, you cannot connect directly to the optical audio on the TV.
#3 Can a non headphone wearer hear the TV at the same time
Yes they can. My husband is hard if hearing and wears them while I listen to the TV volume.
#4 Does the transmitter have to be connected to tv with a cable?
Yes, a single cable is connected to the TV mic out let. I had to refer to the TV handbook to find the mic out let.
#5 Do they have a volume control on the headphones?
Yes! There is a volume control on the side of headphone - easily accessible when in use.