Yes, BPS Pro works fine on any type of Hosting (htaccess files do not work on Windows IIS Servers), BUT if the Server is DSO configured than that changes everything. See this Topic about BPS Pro compatibility with DSO configured Servers and extra BPS Pro setup steps required for DSO Server configurations.
Not a stupid question at all! Yes, you can install it on a dedicated managed server—just make sure your provider offers the right setup. If you’re looking for reliable dedicated server hosting, HostNoc has got you covered.