Use the “Categories” widget that comes with WordPress. Just drag it to the sidebar where you would like it.
As for the second item, try this plugin: http://wordpress.org/extend/plugins/enhanced-meta-widget/
There are actually a number of plugins that will allow you to customize the meta widget.
Moved to Support for better/faster response. (Please take a moment to read the forum rules. Thanks.)
Good luck. Let us know if you have problems and welcome aboard.
Ken