Database updates Out of date
Yes.  Go ahead and run update.php.  It will run the updates (which are usually but not necessarily schema updates) for the new modules.

There is no need to disable modules before updating them.  There is no need to update Core first.  You should, however, put the site into maintenance mode before updating the modules until after you run update.php.

You should run update.php every single time you update a module or the Core.