Now it works.
Many thanks for your help and your patient.
I enclose all the steps that I followed, hoping that in a future they can help someone:
1) In app/config/parameters.php I updated 'database_name', 'database_user' and 'database_password';
2) In table 'ps_shop url' I updated 'domain' and 'domain_ssl' fields with www.project.com
3) In the same table I updated 'physical_uri' field with '/catalogo/'
4) Deleted everything in var/cache/
5) Shop parameters -> General -> Enable SSL / Enable SSL in all pages