drupal 7 restful server VS seperate Restful server to access mysql. Can a restful server be on a subdomain
It really depends on what part of your Drupal site your REST service will be an interface to. The Services module provide a great and easy solution to expose parts of of Drupal core and some selected contribs data and feature as REST services. IT also provide a framework to build your own services.

By-passing Drupal in a separated service directly accessing the MySQL DB is only an option if you are accessing custom tables. Accessing nodes (ie. content) directly in the MySQL database is a bad idea. The DB schema to store the nodes is dynamically managed by Drupal (the Field API). It could change whenever you add, remove or edit fields or when updating Drupal. But the Field API is not the only one to manage node data, any module can contribute data to a loaded node or add behaviours on node CRUD operations. If you go directly to the database you loose all these added behaviours. The same is true for most data handled by Drupal.