I have begun to explore office live small business web design tool, as well as the templates within expressions web, I also have a hosted site with a thirdparty that provides site-builder, .. My question is can I publish with the office live small business web design tool to my existing hosted site?

Some site builders require certain hosting criteria for the resulting site to work/display properly. Pages made in Yahoo site builder probably won`t work on other hosting set ups other than yahoo hosting, as an example. I`ve never used Frontpage, but I believe Frontpage built sites require hosting that allows frontpage extensions. Your best bet is to get a template or custom made site that will work on any Linux based web server, as they`re less hassle to create and set up, and can easily be mo...

front page is a web editing tool like dreamweaver.  it is not necessary to have front page extension compatible hosting to use. there are free templates online, search google.