If you installed Elgg using "localhost" as site url you won't be able to access the site from any other computer. "localhost" always refers to the computer you are sitting at.

The uservalidation plugin wouldn't require any configuration for the email sending to work. Elgg can either make use of the server's MTA/mailserver to send the mails with (php mail command). In this case you wouldn't have to make any configuration settings in Elgg at all. But you would need to set up the mailserver in XAMPP (never used it, so can't give any guidance here). The other possibility is to send mails of Elgg via smtp making use of some other mailsever that offers smtp. In this case you would have to provide the smtp server details in elgg-config/settings.php of Elgg (e.g. server url, username, password, port etc.). The smtp server might accept only mails to be sent if the sender email address matches the server domain, i.e. the site email address you use on your Elgg site would have to be of the same domain (e.g. a gmail mail address if you want to make user of gmail smtp). But as I said, the activation link in the validation email can't be used from another computer if localhost is the site url.