Best option to extend user profile If I want to add a new tab in the user profile page, let's say /user/%user/resume, should I create a new node type and render it in this tab, or should I declare a table describing a résumé per user, develop add/edit/delete forms and render them in this tab ?

For now, I implemented the second options and I am wondering if it would be easier to do it with the Field API by mapping my SQL table to an entity so that I don't need to create all those add/edit/delete forms. So I have a page callback for /user/%user/resume selecting everything necessary in the resume table and rendering the selected informations with a template.

The sub-question would be : should I always map my SQL tables to entities to benefit the Field API functionalities ?

Thank you,
with Drupal you should never have to deal directly with tables and add/edit/delete forms again - Drupal does it all for you. 
In your case you could either extend the user profile and add a "resume" field or you could add a "resume" content type and use the reference module to reference it to the user.