I think your photo is considered Board and Batten and yes, I did it in my previous house.

The wall was the ‘background’ of the board instead of a wood board. It was all painted the same color.
We put chair rail on top and the vertical strips dividing it down to the baseboard.

Placement of windows does not interfere with your installing authentic wainscoting.

Do you think it would look ok without the vertical boards? Just using baseboards and a chair rail?

Absolutely. Typical installation is to use just the chair rail. Adding paneling is simply another option.

You can do white below, or the same color as above or dark below and white above. Your house, your call. No rules.

Again, personal taste, but when the dark color is below the rail, I like the rail to be the same color.

Thank you!!

This is an example of why I think batten board would be challenging... my wall space is not symmetrical... it varies in lengths around the room and is broken up with windows.

Check out Sarah R's work. This is her go to. Slap a chair rail low or high gives you are reason to have more than one paint color. My mom did wall paper below back in the day. Some people just tack one by two strips to the wall below the chair rail then paint it all out. There are options. And it's your house so do what you like.

Well, that is one gorgeous room. Know what I think? You don't need any wainscoting. Room is perfect as it is. Plus, the columns and beam have a paneled effect.

One little thing...next time around buy a bigger rug. You want to pull the chairs out from the table and keep all four legs on the rug.

My 1910 dining room has 3 windows, 4 doors, a built-in hutch, a fireplace, AND the room has a clipped corner, yet they still managed to pull of boar-and-batten panelling. Look at the first image Judianna posted (her first post; black wall over tall board-and-batten). It's not obvious at first glance, but the spacing on the battens isn't even. Once you're looking for it, the last panel on the right on the back wall is significantly narrower than the others. I think if you went in with a measuring tape you would find that the spacing between the panels to the left of the windows doesn't match what's between the windows, either. The thing is, for most people those differences don't register unless you are really looking for them, and even when they notice they don't find it bothersome because the panelling is just one of many thing in the room that is irregularly spaced or asymmetric. My point is, you can fudge the spacing where you need to and it will still look good.

Thank you all for your kind words and advice!!
Julianna, I'm planning on replacing the rug with a 9x12. Trying to find the perfect rug... it's a work in progress! Thank you!