Not sure its particularly smallholder friendly, but used cooking oil burns well. If you're not doing anything else with it, soak half burnt -charcoal sticks in it, burns well.
I would have thought that conkers would take a lot of drying out? I collected and tried to burn beech mast once, but they smoldered as I hadn't dried them enough. - The shells of nuts burn well, but the nut themselves have a lot of moisture as well as energy, I'd guess you might need to split them all open to dry, but have never experimented.
Again, at a guess, I'd say if they were well dried and added to a decent fire that was already up and going, I wouldn't assume they'd cause too many problems to your lum.