I live the Roman shade suggestion, but combine with drapes that can be closed as well...either different heights to accommodate the 2 different window heights or just above the highest window that will extend over the 2 smaller as well.

You need a solid rug with all that pattern. Pull a color from the chairs, probably the lightest one, and go there.

No, the rod should extend about 6" past your window trim and it's more than likely you will require at least 2 panels on each side of the window unless the panels are made for the size of your windows. https://www.halfpricedrapes.com/mirage-gold-green-red-designer-striped-faux-silk-curtain.html https://www.overstock.com/Overstock-Liquidations/Exclusive-Fabrics-Signature-Stripe-Mirage-Faux-Silk-Taffeta-Curtain-Panel-As-Is-Item/12804587/product.html I like these curved end rods so that you have no light leakage from the side profile. https://www.amazon.com/Umbra-Twilight-Room-Darkening-Curtain/dp/B00FB6N9G0 https://www.wayfair.com/keyword.php?keyword=room+darkening+curtain+rod

I am not opposed to valances, nor do I let what's in style overly sway me (at least I hope I don't? :)). Valances can add that custom touch that "finishes" a space. I'm just not sure your space "needs" them. Do you find your windows look unfinished or too bare? If considering valances, I'd opt for a fabric with some colour to it. Unconvinced the grey panels you've posted will add enough texture and colour to elicit a "wow" after all your hard work. As for the overhang, how about testing it with scarves or t-shirts (whatever fabric you have on hand) to see what length make proportional sense to your eye without blocking too much light?