is the refill bottle included?

If by refill bottle you mean the squeeze bottle. Then yes last time I bought it, it was included.

is it non conductive?

That is a good question, I don't know. I have spilled a little from time to time, but I would keep that to a minimum. Typically the filling hole is far away from sensitive parts. Only refill with the power of (not sleep mode). So you can clean if needed