Chimney that old is probably not lined.
Even if it was, I bet it’s a mess, based on your history of “maintenance”
If you have CO detectors (I’d make sure you have a few) you can probably let it go until spring.
You can have an inner liner put in. You should probably do that regardless.
Not sure what was inspected where one person cut something away from the flame and yet didn’t see inside the boiler. You should replace the rotted pipes, tape might not be sealing good.
They should have taken the top off boiler and brushed out the heat exchanger. This is the longest part of the job. Messy too. And critical.
It’s common for bolts to rust up. They usually turn. If they snap, they can deal with it.
Sounds like you need a better service company.
When you said they tapped up the rotted holes on the flue pipe that was a red flag to me.
For the record my 1996 house needed work on the liner !!