Can I do this with WordPress?

I have been asked to modify a wordpress install and I am not sure if what my client is asking can be done as I am not too familiar with WP, if anyone can point me in the right direction it would be appreciated.

1) The site has categories in the top bar and they are hoping that once in a category, I can display only the sub pages of that category in the side bar/widget?

2) Can what a widget shows be dependent on a category, they want to show different widgets based on the category the user is in. Just things like news flashes and contact us….

Any help or advice is appreciated.