Let me start by saying, there is no correct way, but instead preferences and practical concerns. So the only way I can answer these questions is from my point of view. Other decorators and designers may disagree.
A woven shade without curtains looks best mounted inside (above) the frame. It looks more finished. However, if it's for a cottage, cabin or beach house and the goal is a super casual look, an outside (below) mount is fine. Just make sure the cut lines up with the outer edges of the molding.
A woven shade with curtains will depend on the following factors: Style, mouldings and budget. Often the latter being the key consideration. Many woven shades can be purchased "off the shelf" to fit the most common window sizes and if you're working with a small budget, this can be a good solution.
If the moldings are beautiful, an inside mount is preferable. If the casings are plain builder basic or very narrow, a custom outside mount is probably going to look best. I also think one large custom shade for a double window looks simple and beautiful.
Shades (or blinds) for hard to reach places, such as a two story foyer can be put on a remote with custom settings for light control. I have such a set up and it was worth the splurge, especially since the window directly lines up with the hall bathroom. It's the perfect solution to keeping my teenage daughter from view of the neighborhood!
As much as I love mixing high & low, rustic & elegant, this woven shade is just too casual for my taste. I think it's identical to the one in the cabin above and it just looks like the budget fell short.
I find it so distracting to see "stripes" of varying materials such as moldings, rods and shades, when all that was needed to have a more finished look was a simple adjustment in length of the curtain and height of the rod.
This is better...
For a tailored or more seamless look, bring the shade up to the curtain rod and the rod up to the molding.
To my bloggy friends who emailed asking if I was MIA...had a little collision with some ice on the driveway. Sprained wrist...nothing serious, but it's put a damper on my blogging efforts....can't type worth a crap...more than usual.
Images courtesy of Canadian H&H, BH & G, Southern Living, Ashley Whittaker, Cottage Living