How to prevent non-English characters from turning into jumbled words? Whenever I move database, even within the same server the non-English characters change into words that are unreadable. My site is not multilingual (it will be in the future) but users post products titles with accents and in French, Polish or another language. How do I retain the characters and prevent the jumbled words? Thank you.
This is a bit of a guess, but it sounds like some part of the process isn't UTF-8 clean.  If Drupal is displaying everything properly, then it sounds like the database actually is UTF-8.  This leaves phpMyAdmin.

I would log into phpMyAdmin with Firefox.  Right-click, and do View Page Info.  Make sure the encoding say UTF-8.

Then install the Live HTTP Headers plugin.  Download a backup and restore one with the plugin running.  Make sure the Content-Encoding is always UTF-8.

If any of them aren't, then you have some server-specific configuration to fix.

Personally, I think phpMyAdmin is a terrible tool and a security risk.  I use the legacy MySQL Administration Tool for most of my server work and a fair number of backup tasks.  You can also try the Backup and Migrate module for taking and restoring backups.  You can also use the sql-* and/or bam-* commands in drush.