Hello all. 08 oxygen blue base cooper. 152k miles

I'm having a bit of an issue. I'm getting misfire codes primarily cyl 4, but will throw others as well. Changed plugs and coils. Does good until it warms up. At lights and stop signs it will chug, and try to stall. But while driving over 15 mph it is fine, drives like a normal cooper. When it does this it throws the knock sensor code, and occasionally O2 sensor, front and rear o2s.
I have read that valve seats can come loose, but on every cyl, and wouldn't it do it while driving above 15 mph. Clearly at a loss here.

Backstory: got it off of a guy, who gave it to his daughter to drive until she went to college he says. He did oil changes, but didn't use oem or decent ones. At some point the timing was done.

Oil sensor was replaced, started after this. Also seafoamed twice.