WordPress Maintenance Tips

Change All Your WordPress Passwords (Super Users, Database Password, Hosting Company passwords)
Create and test a Complete Backup of Your Website (important to test the backup to another similar env)
If you run a Commercial site see the law if you must keep a backup every month or other period of the time.
Check and Update All WordPress Files. (See if you must update your plugins, theme, and Core Wp, always use a child theme. In case you need to translate a plugin to your language, send the language file to the company that produces the plugin. Alway before updating use a test env and take a backup.)
Check and Delete Spam Comments, bad users, and bad mail list entries.
Test All Your WordPress Site Functionality.
Optimize the WordPress Database. (there are plugins or use the PHPMYadmin by selecting all the tables of the page, clicking the small box, and choosing from the list of table works the word optimize)
optimize images or using a plugin or using a FREE online site
Run Performance and tests for bugs.
Fix the broken links
cheks the logs of the site

You can use plugins like the below, to set the site in maintenance mode

There are also paid services for maintenance, please read the article