I've got a small network of websites, and on-site "A", Let me incorporate a sidebar code to show recent posts in the relaxation of my network, minus site "A".

I have seen icons that possibly do that, however i avoid using icons during my theme.

Let me include:

URL, Title, Blog Title possibly, and Thumbnail Image.

You are able to really see a good example here: http://boston.barstoolsports.com/ (warning, not so SFW)

Around the sidebar he lists "Around Bartsool" that is pretty much like what I am striving at.

Thank you for any suggestions

this wordpress plugin will prove to add featured images for your RSS:
http://wordpress.org/extend/plugins/wp-rss-images/

then just search for a reliable RSS readers
http://wordpress.org/extend/plugins/
have no idea if this sounds like the thing you need? http://wordpress.org/extend/plugins/miro-hristov-rss-reader/faq/