Left field suggestion, also: Make sure there isn't anything trapped under your build plate. If you have any shreds of filament or flakes of old supports or whatever between the steel plate and its magnetic base, the surface won't be flat to a degree that the auto leveling probably won't be able to deal with it and you'll get all kinds of crazy unpredictable results.

I did this on my Qidi once. I'm glad I noticed before going crazy with troubleshooting. I had black filament scraps on the black magnetic base, which were practically invisible and I only found them by feel.

Looks like leveling issue indeed. In some places nozzle scrapes the filament from the bed being too close and piles it up and in others the distance is too high so it doesn't expand enough on surface when leaving nozzle to connect with adjecent already printed lines.

My first impression from the adhesion issue (which doesn't appear to be the main issue of this post) is that you may need to clean your build plate. But considering it was relatively good as it is, I assume you did and the few spots may just be accidental touches to the surface. In either case, their guide is here: https://wiki.bambulab.com/en/filament-acc/acc/pei-plate-clean-guide

As for the extrusion issue - considering the apparent randomness of it my guess would be either an issue with the filament or a partial clog.

Need more information to properly diagnose. Is this a new issue? Are you using auto build leveling for every print? Have you tried cleaning everything and rerunning the system calibration? A lot of different things can cause similar issues and it's hard to diagnose from images alone.

Has it always done this or is this a new issue? I agree with what someone else said, I think this is likely a bed leveling issue. The P1S uses pressure sensing using it's nozzle for bed leveling. If the screws holding the hotend in place aren't tight enough, it might be giving you poor readouts. This could happen after a nozzle swap if you've done one before. Same if the print head itself has a lot of play in it for some reason, it would throw off the results.

Check your extruder tensioner and calibrate bed level?

@Mr_Mofu I don't see the evidence of over-extrusion there. It may be the case that your nozzle is fractionally too close to the build plate, which will often cause ripples (or in extreme cases, gaps) as it pushes filament aside, and may be pushing already-printed areas off the bed. You may also get blobs as material scraped up is redeposited, which in turn can push more printed filament off the bed.