For me it depends on the trim. If you have no trim or it's blah, go ahead and hide it with outside mount. (But IMO it should be fully covered - half-covered it looks to me like someone just slapped up off-the-shelf blinds that were the closest available measurement. But that's me.) If you have great trim, inside mount to show it off baybee! :-) As for whether to go 6-over-6 or 6-over-1, that depends on the style of the house - IMO some houses have 6-over-6 windows that should NEVER EVER have been allowed to be installed, they're just so wrong for the style of the house, and plain 1-over-1s would have served the house so much better. (Why do so many houses these days look like they've been mugged by half-soused window and siding salesmen? So strange!) If 6-over-whatever is truly appropriate to the style of the house, I personally prefer 6-over-1. It's less busy, it's a nicer view out the lower sash, and it's certainly easier to clean. Yes, you can get windows with the muntins between the panes, but IMO that looks downright weird and you can't change the color of the muntins without replacing the entire glass unit. I have a couple of doors like that and look forward to getting rid of them. Snap-out muntins can break easily IME and can warp off the surface off the glass so they look very obviously stuck-on. My last house had them - we took them all off and threw them away.

By casing, are your referring to the decorative molding around the front of your window or the the inside framing (called the sill)? I would measure exactly where you want the side edges to stop and buy that width. Their instructions refer to those instances where you want the rail to be at the top edge of the window. They just want to make sure you're hitting wood framing when you install the headrail and not the edge of drywall. Even if you wanted the side edges of the WT to be the same as your window opening, you would then hang the rail higher so that you were were mounting it to a more solid backing. Make sense?

If you have the depth, inside is best.

To answer your question regarding mixing window treatments..Yes, absolutely you can mix curtain styles and unify the look with using same fabric or shape. Is this your home? I might suggest painting the window molding white to not attract so much attention to all the windows. I think an attractive solution to the quarter round windows is to mount an upholstered valance/lambrequin on the top portion of window giving the window shape a overall rectangle appearance. It is a DIY project that is relatively simple. You could choose a bold stripe or print and drapery panels in a coordinating solid for your other windows. I like the color of the ones pictured. I think your drapery rod height is fine. It is really a cute place. Good luck.