] First of all, does it jive with 1797?

Kinda. I'd place it anywhere between 1795 and 1803 based on dresses. The trend for simplification from the "Robe Anglaise" was only fully realised in ca 1803. The strange robe that Elinor and Marianne wear at Barton - the peach one at the picknick - actually has an original in Nora Waugh's "Cut of Women's Dress". She dates it to 1795.

Elinor's pelisse at Delaford is probably better for c 1805 than 1797. (it's interesting to see that the same kind of pelisse is used in the Emma Beavan was costumier for. An Emma that's set almost 20 years later!)

] Secondly, I presume that throughout at least the first part of the film, the Dashwood women are in mourning. Exactly how long would one be expected to dress in mourning for a father/husband? Does the film depict them in mourning clothes, or with mourning accoutrements?

Not nearly long enough! They should have been in full mourning at least until London, which is ca a year after Mr Dashwood died (according to the Moody calendar). Mourning clothes were worn 12-18 months for a close family member. Many widows kept mourning for the rest of their lives. OTOH JA wouldn't have sent them to town without it being proper ;) Or rather, Elinor wouldn't have gone.

The white dresses worn by both Elinor and Mariane at Barton during the picknick with Willoughby are definitely not mourning!

I can understand why Beavan chose to "lighten" the dresses. Who wants to look at drab greys and blacks an entire movie? I must go home to check - but doesn't Marianne in particular sober up after her illness? Ang Lee is good with lighting moods, and the Willoughby-period is golden, almost dream-like, so I wouldn't be surprised if Beavan chose to do something similar.

] Thirdly, I am intrigued by the straw hats, particularly Marianne's scuttle-shaped bonnet. Has anyone any ideas on how one of these would be constructed?

That particular hat is woven, not braided. My guesstimate is that they started with criss-crossed stalks of straw or reeds, and then twisted and manipulated it. It's hard to explain in writing, but think basket-weave.

Marianne's bicorne is a long braid, sewn together and shaped. It would probably look like an upside-down T if "unfolded". The other straw-hats are made the same way.