Ok, Better chuck my 2p's worth, as it's what I do for a job:
There is a see-saw balance between air in vs air out plus burning temp/volume and height of flue. Get any of them wrong and it affects the rest, and the efficiency of the burn.
Then there is the fuel itself, a cheap moisture meter is worth gold - ideal moisture is 15-16%, despite the industry fix at minimum 20%. Too dry or too small, and it will burn too fast and most of the heat goes up the chimney. Conversely, too large or too damp and it will not burn well, temperature will probably be too low for good combustion. 20% moisture means 200 ml water (2/3rds coffee mug) for every kilo of wood that has to be burnt off as steam, = no heat into room. Start fires with spray-paint can sized logs and lots of kindling - an open kindling Jenga pile on the spilt logs with a firelighter on top works very well. Then add the bigger stuff.
Hard wood is harder to get going as needs more heat, but lasts better than softwood. Roughly the same heat from a kilo of each, just a quicker or slower heat release over time. Alder and Silver Birch burn quite fast, although both are apparently listed as hard woods.
Do not burn Willow!!! It produces road quality tar and clogs up stoves and flues at an amazing rate - frequent cause of chimney fires. Not sure about Leylandi, Think I'd give it a miss.
Smoke is unburnt fuel and means something in the balance is not right, and if you have a smokey smell then the fumes are getting out and not going up the chimney = bad health news. CO alarms are pretty good but a lot depends upon their positioning even in a tent. Stick 'em in dead air corners/non-circulation areas or by the fresh air inlet and they are useless, then you become the Canary.
Closing down a flue size at the stove outlet can be done professionally, but has an impact on the draw, and slows it down, sometimes fatally. 60 to a 125 is not good, shuts it down too much.
It's a big technical subject, beset in domestic buildings by a myriad of Regs, all valid & due to historic fatal experience. The barn issue is a familiar outlier one, over 5Kw needs an air supply but is generally overkill, but can be needed. We had an incident once where someone put sand draught excluders at the doors, and a 3-month old baby got hurt.