You may not be able to invite anyone because you have already reached the limit of 10 members per Independent Project for your type of subscription. You may update your Project to Premium to remove that limit.
To see all of the benefits of upgrading your Independent Project or Team, click here.
Also, when adding someone to a project, you must click enter after you have typed in their email address or you will not be able to add anyone to the project. After you have typed in an email, and have pressed the return/enter key, the add members window will look like this: