No, HPD is not a humanitarian organization and is not mandated to provide housing assistance.  This is the responsibility of the municipalities

Properties under HPD-administration may be allocated to people whom the HPD must evict and have no other place to go.

If you are an evictee and facing homelessness, you can apply to the HPD for housing assistance.

No, not at this time.  However, HPD is working on introducing a rental scheme, which will require people to pay rent.

In principle you do not need any documentation to prove you need humanitarian accommodation.  However, your application will be processed quicker if you provide documentation.