No need to apologize ... moodle is a different beast! 
Before you play much more, make full user backups of those courses and download those backups to your local machine. How large are those backup .mbz files? With only 3 courses your path of least resistance is to restore those backups to a newer version of freshly installed high as you can go Moodle knowing that eventually will require some more putzing with this site in the near future.
A goal would be to get to a long term support version of moodle ... right now highest is 4.1 ... but due to hosting you might not be able to do that ... so a 3.9.highest then. Which leads to ...
Does/Can hosting provider move account to a shared hosting environment that has Terminal/Git? Yes, that will cost more.
When you log into cPanel, do you see a Terminal icon? a Git icon? In right column of the cPanel screen what does it say for DB version? specs? Inode limits? Exactly what DB server running? and version? What is the highest PHP avalable to you?
When providing information, you have to be more precise and know ... not 'seems not to have'. Uhhh ... a theme is a plugin!
'SoS', Ken