I removed an existing overflow cover and noticed there is a blue color gasket behind the tub hole.





I have only seen thick black color gaskets like this.



but this blue color one looks thin. Does this look OK or should I try to nudge the pipe back to install a thick black gasket?

One other question, the new overflow cover I have comes with the two 1/4"X20 machine screws but also a metal pin as shown in the picture below. What is this metal pin for?

The pin's a cotter pin. You insert it through a hole then bend out the ends to keep the thing into which you insert it from rattling out. You must have a place for it to go. I don't see anything likely in your picture.

the upper rod in the linkage attaches to an arm on the overflow plate and that pin secures it

Regarding the blue "gasket", it looks like a blue pipe to me.

[www.amazon.com]

Not a pipe, I nudged it with a flat head screwdriver and it's spongy.

Besides the elbow fitting is PVC and cemented to a PVC pipe, can even see the purple primer inside.

Ah that makes sense, so I don't need it. I wonder why they it included the pin with a cover kit that is completely flat (not to be connected to any linkage).

It was cheaper to 'include it than nake separate bags for trip levers and blank plates.