Help with Gen 3 installation

I just got a third generation Nest and I'm hoping to install it myself. Here are photos of my current setup] and here are wiring diagrams as crudely drawn by yours truly.

I have a few questions I could use help with

• Any idea what the mystery box might be that has a wire coming from common and W/W2?
• Is it okay that the common going to the humidstat is running via the humidifier?
• Is it still ok if I use that same common for the Nest?
• This Nest post mentions that if the humidistat has two wires that I may need a relay. But if one of the wires is just a common would that still be necessary?

Thanks in advance.