i would invest in the manometer . you can see by reading it every day if the trend is less draft during normal operation and this will be a clue that cleaning should be done soon, kind of an early warning rather than waiting for the co detector to go off. besides setting the baro weight, it would also be used to take a reading over fire and then on flue pipe to make sure you aren't pressurizing the fire box so the exhaust is looking for alternative escape routes than the flue pipe.
on stokers, there is a fan that blows combustion air to the coal to get o2 to the fire. some have supplied a pipe from the outside to this combustion fan so that outside air is used rather than pulling air from inside the house.
as for cleaning, shop vac is a good start, the holes in the grates should be inspected, reamed with a drill bit if necessary. fans should all be cleaned, the power vent, the combustion blower and the distribution blower. on my comb & dist blower they are a squirrel cage style and the cage "fins" need to be cleaned seasonally with a q tip and air compressor. i have some filter material on the intake which helps keep them clean. i don't have a power vent but others here can give some tips on cleaning that out. gaskets around doors and around hopper / stoker should also be checked and replaced if necessary.
as mentioned, the flue pipes should be screwed together, 3 screws per joint. i seal my seams with flex furnace cement, but they should fit together tightly enough that this is optional.