Restoring a MySQL database
It is not safe or reliable to ftp the files in your MySQL datadir while the MySQL server is running. MySQL keeps part of the data and metadata in memory, and writes them to the files on disk asynchronously. If you try to copy the files, this takes a non-zero amount of time, so you are likely to copy the files while they're being updated by MySQL Server. So you get the early part of the file before the update, and the latter part of the file after the update. The result is potentially an irreconcilable corrupt file.
A simple Wordpress blog is likely to have low traffic, so it's not like it's in a constant state of update. But the risk is still there.
You should work with your hosting provider to give you temporary ssh access. Or ask them to stop MySQL Server on your behalf.
And yes, make backups of your MySQL database regularly. I use jetpack.com to run automatic backups for me.