Door card removal?

That first photo you posted is missing the push-pin. There's a plastic push-pin with nibs that grab on to the holes in the door to hold the panel. The push-pin sides into the key slot on the door card (so they are removable and can be replaced) and is held tightly, then you fasten the card by aligning the pins with the black door holes and pushing until it's held securely.

It comes off reasonably easy, but I'd recommend using a plastic trim removal (prybar type) tool to assist. By getting the tool under the door card as close as you can to where the push-pin is and prying, you pop the pin straight out. It comes out easier and isn't damaged that way. If you don't pry with a tool or be very careful to remove the card slowly and evenly on all sides, you can put sideways force on the pins that can twist or damage them.

If you pull straight off, the pins should be reusable. They can take some abuse and still work fine. I bought a few replacements (someone had removed the driver's card before and broke a pin in half, and also lost the cover to the door handle screw) but used most of the old pins.

It needs the double nail head so it can slide sideways and lock in to the key slot in the door card. Kind of hard to describe, but you'll see when you remove it. The pic I just posted is the correct part.

They definitely look correct

Damn that looks sexy! Us Americans are stuck with the side airbags. 😒