Display your last Swarm checkin as a map widget in the sidebar or embedded in a post or page, fully authenticated via OAuth 2.0.
In short, very easily. But before you read any further, take a look at Asking For WordPress Plugin Help And Support Without Tears before firing off a question. In order of preference, you can ask a question on the WordPress support forum; this is by far the best way so that other users can follow the conversation. You can ask me a question on Twitter; I'm @vicchi. Or you can drop me an email instead. I can't promise to answer your question but I do promise to answer and do my best to help.
In the current version, no. In the current version, you can link a single Foursquare account with your WordPress site (multi-site or network sites may work, assuming each site is for a single user but I haven't tested this). The plugin is currently designed to support a WordPress site which is used for a personal blog (in other words, exactly the way my site is set up). Future versions of the plugin may support this if people ask for this feature (assuming anyone apart from myself actually uses it!).
wp_quadratum_strapline filter is for just this purpose. The filter is passed the default strapline as well as the URL to the Foursquare venue checked in at, the name of the venue and the date and time of the checkin as a UNIX timestamp. See the Filter Support And Usage section for more information.
Totally; this plugin is licensed under the GNU General Public License v2 (GPLV2). See http://www.gnu.org/licenses/old-licenses/gpl-2.0.txt for the full license terms.
WP Quadratum is named after both the Latin words quattor, meaning four and quadratum, meaning square.