There are several FB apps, which you may use for your eCommerce purposes. However, I would to tell you that in order to meet all of your requirements, you may have to opt for more than one FB app.
If you check on the Internet, you will find several FB apps. Go through their features and what they are capable of doing. If you can find a single app, which can almost fulfill all of your needs, then there is nothing like it. However, if not, then obviously you need to go for more than one app.
There are many apps available on FB, you can share on other social sites by connecting them together to promote it more, you should first create a page and keep it update regularly and target on relevant apps and pages.
[edited by: lorax at 3:48 pm (utc) on Dec 13, 2012] [edit reason] no link drops please [/edit]
I am just curious - I use FB too engage my customers. I don't find it that great for commerce although I will run some specials. I find it better for relationship building. Has anyone had a positive experience selling on Facebook?
@Tonearm - your screen name would be perfect for a guitar player or violin player!