I’m currently developing a Drupal website with a couple of people on Git; it is important that this website would be using the same database without the path because each developer has the dev version on another directory.
How should I do it?
Perhaps I should make Drupal work with SQLite on the development only; then we could add the SQLite file to the Git repository.
Instead of working at the database level to store your site components, use code. Drupal has now great supports for exportables for views, content type, fields, input formats, etc. with the help of the features module.
See The Development -> Staging -> Production Workflow Problem in Drupal and the Code driven development: using Features effectively in Drupal 6 and 7 presentation.