Artist mentioned using a nib pen in post #6873008, though I can't say with 100% certainty that it's also used here.
I can make out most of the text on the implement shown in the picture on this post: On the body is "激しく振るとインキがもれる場合があります" ≈ "Ink may leak if shaken vigorously" On the sticker, I can't read the third character but based on the rest, the sticker refers to water-based ink.
Based on that, it could be a fountain pen or roller ball (but not an oil-based ballpoint) which use the same sort of ink as a nib pen. It may not technically be a nib pen but I believe that is the closest medium tag we have.
His weapon is a Lunacy. His Skill 3 Consumes your Enkephalin and gives bonus Lunacy for clearing the stage, but you have to immediately pull it on the standard banner.
While I can't translate, I do know what scene is being drawn here. Specifically, this is one of the interactions you can have with Jigokku in the postgame where she's raving about getting to shake Sidoh's hand. In short, she just met her god and is losing her mind over it.