What type of bed are you using?
I’m using the Creality magnetic bed. It has similar problems, not because I didn’t level it, but because the underlying bed has a bulge in the middle. If you level the corners such that you get good layer adhesion, the middle will be squished.
As for the residue, don’t try to scrape it off too vigorously; that just wears down the surface and causes more adhesion issues. Instead, I made myself a square about 3 layers thick that covers most of the build plate. I use my least favourite filament to cover the build plate with and when you peel it off, it takes the junk with it.
I learned this the hard way when removing prints that needed a clean surface only to discover they had absorbed the residue:
Using the thin sheet describe above to clean the plate: