I did a variation of this when I had two windows so close to each other on one wall that it made no sense to make two pairs of draperies. So I mounted one continuous rod over both windows, then hung a single panel at each end, and a double-width panel in the middle. With the folds, you don't realized it is one panel, but if the panels were divided, I think it would be obvious and not in a good way.

Grommeted curtains, unless the grommets are large compared to the rod, and sit on it loosely, are not that easy to open and close. The simplest option would be a rod pocket sheer, you would just need to make sure you have adequate clearance. However the thing about opening and closing these daily is that one one generally pulls on the curtain edge to open and close them. I think this gets them dirty in that spot unless you are very careful. They do make traverse rods with hooks and a pull rod to open and close them. Look at Country Curtains for an example. Here is a link that might be useful: Track Rod Set

Well, if it were MY room, it would always be the cotton linen. And it would be an ivory or a cream. So since I picked one from each category, I'm not really helping, am I? But you haven't really given enough information. Silk goes with a more formal style, perhaps even a more feminine room. Cotton works better in a more comfortable setting and could even be used to work in a more masculine themed bedroom. So I guess I would need to know more about your style, your furniture, and whether you want your room to be a more soft look or go more crisp and contrast....and that's just to start! Red

While they do sell a grommet just for this, if you don't have it, I would sew a ring behind the fabric, between the last two grommets near the lead edge and hang it from the ring. You could also use a drapery rod ring and hang it on the rod between those grommets and hang it from there, again on the back side. You don't want the wand to be on the room side.