Does Apache Solr separate searches with multiple sites on one server?

There are a couple different ways of doing this. You could set up different indexes for each site, you could use a module like apachesolr_multisite and limit the searches to only that site, or you could write a couple hooks in a custom module that add a site_id field to the document in hook_apachesolr_index_document_build_node() and another to scope searches to just that site_id in hook_apachesolr_query_alter().