Lumia has the fragment IEMobile in the user agent so it should be detected as a smart phone and the mobile skin should be applied.
You could alter the config setting but it should not be needed so I don't know why you are not seeing the mobile skin.
The relevant config setting has a comma separated string of user agent fragments (lower case) like this:
<add key="MobilePhoneUserAgents" value="iphone,ipod,android,iemobile" />
The iemobile fragment should be sufficient but you could add lumia or the word phone:
<add key="MobilePhoneUserAgents" value="iphone,ipod,android,iemobile,phone,lumia" />
As far as styling, yes you can override the css just as with any other skin, though the easiest way to style it is with jqueryui themeroller since it is based on jqueryui. Probably best to work in Firefox with the user agent switcher while working on style so that you have the benefit of viewing the source of the page and using browser tools to see what css rules are applied.