go to your dashboard and click on updates in the left hand menu. if you need to update anything it will tell you there, don’t bother going through core files to find that kind of information.
All “update this” notifications are disappearead for old version themes and plugins can’t update anything.
check your wp version in wp-includes -> version.php
as for not being able to update anything i can only assume that the version you’re running is quite old and nothing’s compatible anymore…
if that’s the case you may need to download your database, scrub the whole site and rebuild with version 4.0 and upload content back into your new database.
$wp_version = ‘4.0’; in version.php
Is there anything I can do before clean WordPress install?
back up everything, database and root directory. you can easily do both via cpanel on your web host. also do an export of your site via the dashboard (tools -> export) as you could try using this to import things into the new one rather than having to go the database route (that requires changing settings in the config file and in the database itself.