How is Lauterbrunnen in early Nov?

I'm thinking of visiting Lauterbrunnen in the 1st week of Nov. Have read on some forum pages that most places are close. Would like to find out:
1. if most places (shops, restaurants, hotels, sights) are really close during early Nov?
2. Will there be water cascading down from Staubbach falls?
3. how is the weather like? will it be too cold or foggy to go on hiking/trekking?
4. How are the fall colours there?
5. if there are any other places that will allow me to enjoy some nice hikes/trekking and fall scenery?