Hi Nitzan.
On your second question "Does any experience other than "project manager" qualify as eligible experience for the application?"
A job designation is vital in the workplace but for the PMP exam application; your job description does not have to strictly read "Project Manager". For PMI, you need to demonstrate that you have been involved in projects in the 5 phases of Initiation, Planning, Executing, Monitoring and Control and Closing. A most important rule of thumb to consider is to always have documented evidence of the projects you put in for consideration so that you can avail them to PMI in case of an audit.
Best.
Eric.