Hello! I no longer use styrene for my mouth-plates on my new builds. I recommend something like a gasket rubber; that’s basically a thin rubber sheet. It’s much more flexible. I’m not sure where you’d find it where you are, but I get mine in small pieces at the hardware store near the plumbing section.
As for your questions:
1) I do put stuffing in the neck area of my builds, and a shaped piece of foam for the top of his head, but this is only to give his head shape while on display. When you use it as a puppet, there should be no stuffing in the head (kermit’s Head shape is basically the person’s hand). It really depends on if you want to build a puppet Kermit, or a “poser” puppet, like in the photos you showed above. That one basically does have wires, foam, and stuffing inside to give him shape and a posable mouth.
For display, I do this with my puppet builds:
View attachment 960190
2) If you want his mouth to be posable (non-puppet version) then yes, I add wires to the back side of the mouthplate to allow it to open and close. I’ve made one version with the wires in his body for my ‘poser’ kermit, and I also add a thicker wire from the bottom of the mouthplate that does through his body—basically like a spine, where the arms and leg wires also connect!
But my puppet versions just have the removable stuffing and foam you see above. I dont put wires in those, so his mouth just kind of stays kind of open naturally when sitting there
Below is a photo of my “poser photo puppet” with wiring inside. Basically, in this one there is wiring that connects his arms, legs, mouth, to a spine in the center that connects to the bottom of his mouth-plate.
View attachment 960192