Page templates and widget sections with TwentyTen

I have just started setting up a web site and am using TwentyTen theme as it is close to what I need. Most of my pages will be static; actual use as a blog is limited to one or two small sections. I’m a beginner with customizing WordPress so am somewhat lost in all the flexibility.

I have two perhaps related questions:

1) Generally, wordpress uses the same sidebar on all pages, so the same set of widgets appear on all pages. I would like to use different widgets on pages with different templates. How might I accomplish that?

2) Twenty Ten includes two templates: default and one-column. Can I add more templates (if I need to) in a child theme rather than modifying Twenty Ten itself?

Thanks!