If a home page must be .html how can a master page be used throughout the site?  When trying to apply the master to the home page I get the message that it needs to be changed to aspx.

A home page does not have to be html. In most control panels you have the ability to set the default page. With other web hosts you may have to ask tech support to change your default home page.

In my experience web hosts that do not have a setting in the control panel you can change the default page name/extension have a series set up. In mine it is index.aspx, index.asp, index.php, index.html and index.htm. Others I have seen have default.html, default.htm, default.aspx, default.asp, default.php.

 If you have the later type setup and have an index.html page then it will show first. If you are using the FPSE to publish whatever is the first listed page what Expression will want to choose. You maybe able to change it if there is an order of preference extensions list like I am showing above by right clicking on your index.aspx file in Expression Web's folder view and selecting "set as home page". You may get prompted "Are you sure you want to change the home page ..." If so, say yes so Expression won't try to change it when you publish to match what the fpse say.