The file count on my hosting is higher than it should be

This can happen from PHP session files not getting cleaned up automatically which can happen with PHP 7 and the custom session handling. Basically a session is a text file created when someone visits your site to keep someone logged in, remember cart, etc... 

To change this do the following: 

1) In your Sytist admin click Settings in the main menu. Then UNDERNEATH the left menu click edit config file. Look for the following line and delete it: 

ini_set('session.save_path', $setup['path']."/sy-phpsessions");

2) Next using your FTP program or the file manager in your hosting control panel delete the entire sy-phpsession folder which contains all the session files.