Yes, the upgrade process requires you to replace all the old version files with the new ones. We highly recommend you to create a backup of your old files so you can restore them if necessary. Also, note you will need to use the old
config.php file with the new app version, as it has all the required configuration to continue using your ResourceSpace database.
The database won't change after replacing the files. If any additional step is required regarding the database, I think you will be warned in the admin panel of the application or in the release notes. We recommend you to ask for any additional step in the official ResourceSpace forums at https://www.resourcespace.com/help
It is not possible to upgrade base components (PHP, Apache, MySQL) for out stacks, only applications itself (WordPress, ResourceSpace, etc). You will need to install a new version of the stack and migrate your application data to the new one