Nothing is stopping you from hosting your site anywhere else if you have it, however, SQL databases aren’t stored in your website’s files- they’re on the database server. The only way you’d have a backup of your database is if you’ve exported it from phpMyAdmin, as described in the knowledge base article on backing up your website. If you did that the database would be located in… well, wherever you downloaded it (it should be a .sql file, assuming you exported it with the right settings).
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