Try to best describe. On the broke screws shown, I would suspect there is a blind nut hammered into the back side. I would just take a straight punch to the head of the broke screw (topside) and tap them out. Replace the blind nut available at most any hardware store and done. For the rails, a block of wood and flat blade (or screw driver) pry up Slowly a little at a time from both sides back and forth till they pop out. Always leverage from your scrap wood block. Have removed many of these with little issue you just need to go slow. Good luck.

Ok these things may be at odds with each other.

1. Do you really need to remove the guides? Are you just cleaning the machine? You don;t need to remove the guides for that
2. Why do you need to remove the guides? Removing the guides, eXpecially the biff-bars, is really not a good idea unless you're planning on going whole hog and clear coating the thing when you're done.
3. Do you really need to remove the guides? You could end up pulling up paint & playfield chunks like that.

OK so let me try to figure out what you mean. Do you mean you where trying to get a screw off the playfield and the screw broke?
Is it a machine or wood screw? is the screw still sticking out of the wood or is it below the wood?
Pictures might help us help you

Ok I just wanted to make sure. Yes those are called "T-nuts," and you can just remove them from the bottom of the machine, and replace them. You can either pry them out from the bottom if you can get a tool under it, or push them out from the top of the playfield. If the screw is broken just hit the screw with a hammer and it will fall out. New screw, new T nut, you'll be OK.
Most likely, those are 6-32 t-nuts https://www.pinballlife.com/6-32-tee-nuts.html

Or, you might be able to get the broken screws out after removing the t nut and reuse it.

As for stripping the machine, I caution against taking everything off "just to do it." Believe me I say this because ive gone too far myself and wish I didn't!
Leaving the metal guides in you'll still be able to clean and wax the entire thing and it will most likely come out great. Removing them is really not standard for a simple cleaning job.
But either way, we are all hear to help.

Good luck!

For the metal rails, DO NOT pry them from the top side of the playfield. Get a pin punch set (which you will use in many other places on pinball games) and tap them out from the underside of the playfield. Tap a bit on one side, them go to the other side to tap it out evenly.

Something like this: https://www.marcospecialties.com/pinball-parts/77-PPS

I'd suggest leaving them alone.

You can polish them in place, and still clean and wax the playfield with them there.

Depending on the age and manufacturer, the guides sometimes have small fins on them to help keep them in place. Those can rip holes and pull up strips of wood and artwork when you try to force or tap them out.

You are likely to cause more harm than good by removing them.

The only time I ever remove one is for repair if one or both sides are loose and slip up and down. By that point, the hole is usually hogged out enough where removing the rail doesn't really do much damage.