Is it possible to add new project with free account?
Yes, you can add projects to free account.
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Hi @Demis_Lorenzi and thanks for reaching out!
Of course, you can create new projects with the free version of Asana! Here are the steps to follow: Setting Up a Project in Asana | Product Guide • Asana Product Guide.
Note that if you’re using an Organization, you must create/join a team before you can create a project 
More info:
Create a Team: How to Create, Join, and Manage teams in Asana | Product guide • Asana Product Guide
Join a Team: How to Create, Join, and Manage teams in Asana | Product guide • Asana Product Guide
Hope this helps!