Hello - will Premiere Elements 2018 work with this GPU: NVIDIA Quadro M4000? or perhaps QuadroK2200?

Those graphics cards should work fine, but I don't believe Premier Elements uses GPU acceleration. Photoshop Elements does, but I believe only for 'Adjust Facial Features' editing functions. It's hard to find any GPU data on the latest 2018 versions, but that was the case for the 2015 versions.