I can't offer any advice with window treatments, sorry. But velvet seems a bit much, IMHO.

I think one large rug would work better in the room than 2 smaller ones. Maybe an oval or rectangle rather than a square shape.

Is there any other way to arrange the furniture? Right now the seating looks staged and the middle of the room looks empty.

Perhaps a U- shape arrangement would make the room more conversation friendly. You have a wonderful space to work with and your floors are beautiful.

i would treat your windows as 3 separate windows and hang panels on each side of all 3 windows...mainly because there is room and since there is wall and not woodwork between them... i would also hang them above the windows, but below the transoms. i wouldn't hang blinds, unless the view of the other houses bothered you. i would only use velvet if i changed the panels seasonally... otherwise, i would use silk. your fabric swatches are beautiful! i cannot comment on the rug/furniture---think 2 rugs might work, but would have to see your stuff in the room! it'll look gorgeous when done!

Taking your questions one at a time:

Plain, simple panels would work fine in this room.

Either rod placement would work. It's a matter of what you prefer. Question--when and how will you be using this room? If the panels are your only window covering, will you need them to block out sunlight at any point during the day? If so, you should consider covering all the glass. If you are planning on sitting in the room in the late afternoon, you don't want to be blinded by light coming through the transoms.

Again, treating them all as one window would work. So would treating them as three separate windows with the panels stacking in between. Which look do you prefer? Stacking the panels in between the windows will give the wall a softer look, while pulling the panels open to either side will highlight the windows and the light.

The need for shades or blinds depends on a couple of factors. First, how much privacy will you need? Second, will you be closing the panels to get privacy? Once you turn on the lights at night, it's pretty easy to see what's going on from outside. If you are going to use lined panels and close them every night, you don't need shades. If you would prefer to leave the panels where they are all the time, you would want to consider shades or blinds for privacy.

Velvet would not be over the top, if the fabric is made into simple panels. It's not just about the fabric, but also about how the fabric is used. Velvet can look heavy, depending on the weight of the fabric and the color. But so can other fabrics. You can treat velvet casually or formally.

About the rugs--usually I am in favor of two rugs for two seating areas. The rugs help define the space. But given the floorplan as you have it in the drawing, that would create a line of plain flooring extending from the doorway to the windows. I agree that would cut the room in half. If you are going to keep that floorplan, I'd say one large rug would work better. The alternative would be to create one seating area by the windows, anchored with a smaller rug, and a larger rug anchoring a seating area by the entrance to the room.

Personally, I would hang the curtain rod above the transom windows and put panels in between each window. If you want to do velvet I would make sure it is a lightweight velvet. I am not sure I would go with 1 rug though due to sheer size and budget restrictions, if you have them.

Thanks to everyone for the responses.
It looks like a split decision on the drapes. It does help to know there's not an obvious right and wrong.
Bypassing the blinds. The neighbor is much further away that it appears in the pix, and landscaping on the back of our lot will provide additional screening.
Furniture should be here in about a week. I will post again with furniture and hope for feedback on the rugs.
Camlan - I agree about the floorplan. It was not our first, second or third choice, but looked best taped out on the floor and I felt the multiple chairs offered the most flexibility. We always had in our minds that if we hated it or it felt too sparse that we would move the chair in front of the windows to another room and get a short sofa for that area. The windows overlook the pool and everyone gravitates there, so we were hoping to leave the area open.
Djsaw - There are tight budget restrictions on the rest of the room. If I end up with one large rug, it will be an "overstock" find. We built the house a year ago and had carpet in the two rooms shown. Wood was in the foyer, halls and adjoining kitchen and hearth room. I couldn't live with my mistake (trying to save $$$) and convinced my husband to replace the new carpet with the hardwood.
That's why I'm asking for feedback on every little decision....unfortunately no more mistakes allowed : )
Thanks Again.