I'm not an electrician, please consult with one if you're unsure.

I think Shadow is right on both counts.

The wire is very old. Personally, I would rip it out, but that is a risk assessment you have to make.

A 240V circuit, in North America, gets there by having two hot wires one on each of the 120V circuts from the transformer in the street. So no neutral wire is needed to complete the circuit. If you want to think about electricity "flowing" it flows from one pole to the other (instead of to the neutral in a 120V circuit). The unshielded wire is your ground.

This is a decent guide: https://www.thespruce.com/installing-a-240-volt-circuit-breaker-1824649

Please make sure you understand their point about what the main breaker does and does not disable.

Best of luck, looks like you're tackling a tough but fun project.

I can’t take credit for this one, that goes to my brother:

He once tried to smoosh a house fly with a literal ball peen hammer. Suffice to say, the fly dodged with ease, the glass window it was sitting on not so much.

I’m not familiar with pellet stoves, but would a converter work so you can reuse the old exhaust pipe in place?

https://www.homedepot.com/p/Master-Flow-7-in-to-4-in-Round-Reducer-R7X4/202191795

Same here. I know a lot of folks don't like the results, but to be honest, I don't find Google any better these days.