My co detector is mounted about 1/2 way up the wall and about 5 feet from the stove per it's instructions. But it is designed for RV, not household use
But, it occasionally trips off if I am cooking and don't have enough ventilation. It's sorta a reminder to add ventilation if I forget.
For those that try to use the generally unsafe practice of cooking flower pots for heat, it will go off.....
As far as your furnace
, externally vented furnaces should not trip it off unless there is a CO leak and you will want to know about that. I can't comment on older panel type heaters.