Willows would have been coppiced for osiers/withies for use in basket-making etc, yes. I seem to remember reading an article about a farm (Sussex way?) earlier in the week that still does this, although it's harvesting mechanically these days!

As for seasoning wood for burning (as opposed to woodworking), that's variable according to a number of factors. Average temperature obviously plays a part, as will the type of wood. But mostly it's down to ventilation. And under the heading of ventilation comes splitting the wood. If it's left as sawn logs with the bark on, it'll take a lot longer to season. If it's split early, so there's plenty of exposed wood for evaporation to take place from, there's no way it'll take a year. The greater the ratio of surface area to volume, the quicker it'll season, especially if said surface area isn't mostly covered with a water retaining layer i.e. bark! I've somewhere between 1/4 - 1/2 a ton of willow lying around my garden at the mo. I've two trees, both of which took damage in the storm a few weeks ago. Once split it ought to be dry enough to burn by about the start of next year.

One final thing I forgot to include in my earlier reply... In theory, yes you do have a higher risk of a chimney fire with resinous woods. In practice, any increased risk should be insignificant. The two more important factors are, first, is your chimney properly lined? That doesn't reduce the risk of a fire, but it will reduce the risk of serious damage. Most of all, how hot do you burn your fire? When I moved into my current house (nearly 11 years ago!), I had a freshly plastered wall in the second bedroom. The owners lied to me & told me it was water damage. The new neighbour, who had been a charcoal burner, told me truth - he knew what tar smelt like & it was tar damage (they'd ask him to have a look at it). I promptly had the chimney properly lined...

If you burn your fire hotter, the smoke will rise more quickly & cool more slowly, meaning it leaves less deposits before it's outside. The other remedy is Stovax Protector which, as they say, "Attacks tar, creosote and soot in chimneys by converting it into harmless clinker which may be easily brushed away. Helps prevent chimney fires." It's a bit pricey, but I find it effective.