Chris, this video is kind of long, but she shows how to clean the rotary cutters:
https://www.youtube.com/watch?v=h7ACuhS53ko&t=3s
Regarding slippage, have you tried the Slidelock rulers? I absolutely *love* them, and use them both by themselves and on top of other rulers. They stop the slipping and keep my hand high and away from the cutter. One of the best quilting investments I ever made:
https://www.quiltersslidelock.com/slidelock-models/
I got a set of the 2 sizes of slidelock, and I use both sizes a lot. I got the yellow ones, which theoretically make it a little easier to see the edge of the ruler compared to the clear ones. I don't use the ruler that came with the set at all. It has so many lines it is visually confusing for me, and I prefer to use other rulers for measuring purposes. Their other products are newer; I was surprised to see them when I looked up the website to post it here.