Looking at the default theme, it has only one style (style.css) and is loaded in every page.
Will it be possible to create another style and load it for a specific section only, i.e. categories.css for the categories page?
Certainly, but not exactly like that.
Generally, changes to CSS go in the custom.css file of your theme.
You can either create a custom theme: http://vanillawiki.homebrewforums.net/index.php/A_Quick-Start_Guide_to_Creating_Themes
or use the CSSEdit plugin and add css changes via the dashboard.
Using a web inspector such as Firebug for Firefox will show you which CSS elements you need to change, or you can work your way through the examples in the link to the Wiki.
Look at the body tag and you will see that you can style any page differently based on the bodys class/id.
Having two different css files doesn't make sense.