Well, I have installed Poser Pro and tested it. It also has similar issues, but this time exported animation can have picture background, but  no transparent background. Again GRAY background instead of 100% transparency.  Exported PNG pictures still have no background.

And then... I updated graphic card driver from version 190.0 to new 191.07 (Nvidia) and my Poser8 installation went even more crazy...You know that little slider under render settings called PREVIEW TEXTURE RESOLUTION, when it's set to maximum of 4096? Well it went crazy, showing me 4096 but there is no slider. When I try to move invisible slider little bastard reappears, but max number is no more 4096 but 2048 instead, and that's it. Can't revert it to 4096.

REASON for all of this is definitely INCOMPATIBILITY of POSER with NEW Nvidia graphic card DRIVERS.
All my previous animations that I have produced in POSER PRO with old drivers were working fine ( transparent background and image background with no problems). If I could only remember what version of drivers I was using...