Hi there!
I have experience with setting up my own web server and running several websites on the same one, including two versions utilizing the same SQL database.
As for using the two websites on one MySQL database, you simply use the same connection details for the SQL server in the PHP database connection code, and it should work seamlessly. If you wish I can help create backups or have them running on seperate databases if necessary.
Here are some examples of my work:
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I hope to hear back from you soon!