Making the most out of widgets, especially for facebook and twitter updates

I have the following desires to improve my free wordpress.com blog, meaning NO plug-ins, only widgets. Is it possible? There isn’t an option for me to use anything other than a free, easily hosted blog.

1.) Automatically update my twitter feed with a link and short description.
2.) Automatically update my facebook status with a link and short description.
3.) Display the current weather.
4.) Display a map of a region, with a small map of a specific country like this https://4.bp.blogspot.com/_v07zrM8hRis/SYdVqj_cHaI/AAAAAAAAABU/KdamN4NFRsk/S269/senegal_africa.jpg
5.) Display random images from a Picasa Webs account.

I’m wondering if I should just sign up for a Blogspot account to do this, but I really like the layout and dashboard of WordPress.

Thanks!