Resolve spoiling PNG images and effects

Hello. I've recently switched to Resolve from PP+Ae and faced some issues with basic media composing.
Long story short, the first screenshot:
I added this southpark character.png to the timeline. Default resolve transform works perfectly fine, but I often need more than that (apply chroma/luma key to a png picture and so on), like in this case - I wanted to make him casting a shadow. I thought the obvious solution to this is to go to the Fusion tab and make it all in one clip using multiple nodes, but here's the problem. As I switch to the Fusion tab (the second attachment), something strange happens to the playback windows - seems like the aspect ratio became that of a default media (source png image), and now when I switch back to the edit tab (third attachment), the media appears only in that limited area (I suppose the same default aspect ratio of that image) - and I cannot go back — after undo's it stays the same. Same happens with all the png images that have aspect ratios different than the project settings. I've searched for an option to fix it but no success. I'm sure there should be an easy fix to this, please, help.

And one more thing about effects and the media in edit tab. When I apply any OpenFX to the media, Resolve applies effect considering an area of the media only, and not the project. You can see what I mean in the attachments: I applied the shake effect on the png image as I wanted the image to shake, but it only worked within the limited area of original image with the appearing of the black borders. How do I make it work the way I intend?
Is the only way to make it work to start editing with original 16:9 clip and do all the effects, animation, and overlay media in the fusion tab?