First cometchat is not a standard joomla extension as this extension does not save their data into the DB with the joomla table prefix but has its own unique prefix that forbid to have 2 websites into the same DB.
Second, the "installation/install.php" is a detection performed by joomla when it does not find the "configuration.php" in the deployed directory.
In this case, Joomla redirectory automatically the user to the current URL /installation/install.php to allow creating the DB.
Concerning the update of the product, see the FAQ for the procedure. It explains and show with video and PDF how to get a new download ID.
www.jms2win.com/en/faq/faq-joomla-multi-sites#cat-122