How to remove a (press fit?) crank arm from a chain ring?

Sorry, those chainrings are riveted in place. You just have to replace the whole crank arm.

You could drill out the rivets (and later replace them with button-head hex screws) so that you could take off the chainrings. But this would be more effort than its worth. And it's not like you could easily find replacement chainrings anyway.

As @criggie notes, there's not nearly enough rust to make this worth it. Scrubbing the chainrings with chain cleaner and a brush should take off most of it. Those 'rust' marks are places where the chain abrades when the gears shift, any paint you put on them will be scraped off the next time you shift.

It is possible the above responders may be missing the point. In this case the larger chainring and spider is a one piece combo. The question is the press fit of the pedal arm with the spider reversible and what is the procedure and tools required. Not sure, but if it is a part that has questionable safety status where in you have a concern that the part will no longer perform as designed, then it may be a candidate for experimentation.