I have never seen a gradual taper as you describe, probably just because of the technical challenge of building it that way. Here is a design that Koen in Thailand came up with
Gilmore style? - #1019 by k_vanlooken
I think his bottom reactor tubes are only 5 or 6 inches in diameter. His nozzle points upwards, so that helps prevent a hot spot forming on the opposite side. I have always really wanted to build something in that configuration, but I have never been able to find a good thin-walled tube in that dimension.
As others noted an inline blower isnt needed, but If you look around, there are people that have done it with the bigger bilge blowers. I have never really had a problem with getting the char-gas close enough to the intake. Your engine is displacing a lot of gas with each pull, and you can get rich gas through a couple feet of hose in 2 or 3 pulls.
This depends on how you orient your nozzle. A lot of guys now run the air in vertically, instead of straight through the side. My first design basically just had a hole in the bottom of the reactor, and every hiccup in the engine would scatter some burning coals on the ground. Using a leitinger nozzle really eliminates that problem, as anything that falls down stays in the tube. A fine wire mesh cap would also help. Some designs use a nozzle over an ash-pit, but then you need to have some arrangement to light it up at the start.
Cooling large quantities of charcoal in a sealed barrel is a very bad idea. the vacuum it creates is capable of crushing a 55 gallon drum, or at least clamping the lid on so tight you have to drill or smash it open. In hindsight, drilling a hole would have been better than just hammering on the rim out of frustration - so learn from my mistake if you ever do that 
it was a brand new barrel too. Shouldnt be a problem with the gasifier, though, it will find some tiny little leak to equalize the pressure as it cools off.
I am in a similar situation, in that I need to build a shop before I can get too much more done on my woodgas setup. Hopefully it will stop raining soon…