Carrier HVAC: CO Alarm and Smells

I’m trying to figure out the right questions to ask. I’ve not had good luck with a HVAC service company when we first purchased the house. As I don’t think I have any urgent risks given the 3x Nest sensors are working (i.e. they would have to fail on different floors), I’d like to try and get an understanding of potential root-causes before trying my luck with a service company. Appreciate all advice.

Issues:

1. Our Nest Protect CO alarm has gone off twice since it got cold – 90
   days apart, in the basement only. Opening the windows cleared the
   gas and the issue did not re-occur.

2. Separately, near the air-filter area, a strange smell of
   post-processed gas(if that makes sense) is lingering in the air.
   Again, opening a window clears this right up.

While I think the air-filter might be old(?) and changed it for issue #2, could I have a more generic issue of an exhaust valve being clogged that might be causing things to linger? I’m not aware of any physical trauma to the HVAC system between the last two winters – so it’s perhaps some natural build-up?

Thank you.