"When you do chi gong, cannot you just medidate -- sit still -- and circulate the energy around?"
Yes.
"I've never performed those chi gong movements, but I already have some basic skills with manipulating chi, will I gain by doing the movements?"
You have to find our what they are teaching/training with those movements. Their answer will be insightful.
"Now that you have the internal chi circulation, if you know how to use it for martial purposes, do you still need to associate it with Tai Chi or Pagua attack's movements?
For example, if I become very powerful with Chi, can I it to supplement -- for example -- a modern moxing straight punch?"
I would say yes, if you find a good tai chi or pagau school. Using chi energy is only part of it. Internal strength also includes learning a different way of moving your body. Internal strength is not merely using chi. A modern boxing straight punch done the normal way is external.
"My wonder is why does chi gong movement and meditation always get taught together."
From my research into chi gong, the most common answer I've seen is that movement based chi gong is Yang and still meditationis Yin - they seek a balance, so both are taught together. A well rounded internal martial artist, I was told once, will do an equal share of physical movement training/form, standing meditation, and sitting meditation. Each has their own purpose.
~ Eric Putkonen
(Teaching Tai Chi Chuan in Plymouth, Minnesota)