Nope, don't punch that pin either!
THIS is the pin you need to remove:
It's a roll pin, so use a punch that is as close to the exact diameter as you can find, otherwise the pin will be damaged or destroyed. Tool companies make special roll-pin punches, and if you can buy or borrow a set of those, that would be best, but a close-fitting normal punch will do if used with care.
Once you remove the roll pin, pull the slide to the rear about a half-inch to get the hammer out from behind the firing pin, and then you should be able to dump the firing pin and spring out of the rear of the slide assembly (this separate part of the slide is called the "bolt" in the manual). Once you've removed the firing pin and spring, then you can use a hammer and non-marring punch (manual says aluminum or brass, but I think a sturdy nylon punch would work too) inserted in the bottom of the frame (where the magazine normally goes)...
... to tap the bolt up and out of the slide.
CAUTION! You may have to pull the slide slightly to the rear as you tap the bolt upward, to prevent the extractor hook (circled, below) from catching on the rear of the barrel and damaging either itself or the barrel.
Once the bolt is removed, the slide will move forward off the frame (may have to lift the slide's rear edge slightly?). Take note of how the recoil spring and rod fit into the slide, as you'll have to replace them later during reassembly. It's easier to do if you've seen how they were situated in the slide before falling out.
Reassembly is fairly well-described in the manual, and after taking it apart, you'll have a better feel for how the parts go back together. It looks like you're pretty good with that digital camera, so feel free to take photos as you go so you can refer back to them later, if you think it might be helpful. I did this when I tore apart my last vehicle engine, and it makes reassembly go a LOT smoother if you can see what it looked like before you ripped everything apart.
"Placement is power" -- seen in an article by Stephen A. Camp
(RIP, Mr. Camp; you will be remembered, and missed)