Answers

Hard to tell for sure without a close look, but the roofing / waterproofing material looks like TPO, a single-ply roofing membrance.  It is not made for direct traffic, so appears someone has installed rubber pavers over it to protect the membrane.  Not an unusual application.  The membrane should have positive drainage to what appears to be scuppers, and any water falling on that balcony wants to be able to freely drain - meaning, any pavers installed should have a means of drainage on the underside.  Appears to me that these rubber walkpads really do not.

Have a professional roofer /waterproofing company take a look and work with you toward a solution.