I have to say that if I was your developer, I would be a little bit concerned by the lack of trust that is evident in your wish to restrict his access to "some" of your server's files. If it's about confidentiality, that should be part of the contract. Anyway...
It's not possible to change FTP access restrictions unless you have sufficient control over the server configuration, specifically the FTP user permissions. Many hosting providers don't even provide for more than one FTP user - those that do may not permit that degree of customisation. If yours does provide this degree of control, it will be available at the time of creating a new FTP user.
Changing MySQL users and permissions in cPanel is simple. Select the user; select the database; then select the permissions and click to add them.
Info like that is all available on the cPanel website: click here.