Part one.

Picture note: I ran into a bit of a problem hunting for pictures today... the Us didn't name the weapons, but the British did. Seeing as the document I was reading was British, it failed to mention the US designations, and so I'm taking guesses here.

Across the Atlantic the US were also looking at flame weapons and fitting them to tanks. At the time the report was written the Americans were working on three designs.
The Q. Gun was a modification to a M5A1 Stuart, interestingly it was designed so that everything was inside the turret, so all you needed to do in the field was swap a turret over. This was considered about 20 hours work. It replaced the 37mm gun with a dummy gun containing the flame gun. The 100 gallons of fuel, and the compressed gas were in the turret basket. The effective range for the gun was 100 yards, with a flow rate of two gallons per second. To make room for these the turret only contained one crewman.
The Klass Gun was a different matter with its fuel tanks in the sponsons of the tank, and so the entire tank had to be manufactured as single unit. Equally the pipe work running from the fuel tanks meant that the turret could only turn through, at best, 180 degrees unlike the 360 degrees of the Q. Gun. However the Klass Gun got an effective range of 120 yards, and a flow rate of 3.2 gallons per second. Fuel supply was also larger at 190 gallons. Interestingly the Klass Gun didn't have a dummy gun fitted, instead the nozzle was mounted directly into the gun mantle, making it look like an unarmed Stuart. The Klass Gun also only had a one man turret.
The Satan flamethrower... possible Klass gun?
The last design was still under development at the time the report was written, but it had some interesting features. Called the Indiana Gun it carried its fuel in a trailer. The compressed gas was air pumped in via a compressor powered by twin six cylinder aero engines. The flame gun was actually two guns, one designed for long range work, the other for short range work, and these were mounted in an external mount on the front hull. As it was still under development only the barest details are available, that the flow rate depending on which gun would be four or five gallons per second and the range was 125 yards. Its interesting to remember last weeks lesson about mixing compressed air in fuel tanks and how it makes them explosive, and one wonders how well this project would have progressed.
E9-9 possible Indiana Gun?
Back in the UK in 1944 the British started Project D.30, which may (although none of the documents mention this, but the dates do match as a precursor to the Salamander) have become the Sherman Salamander. It's basically fitting a British flame gun in the place of the main gun on a Sherman V. The fuel was carried in the hull, but to maintain the 360 degree turret traverse the fuel fed into a junction box at the base of the turret, this allowed the turret to keep its full rotation, an idea neatly borrowed from the German Panzer III flame tank. The tank was to be fully tropicalised, and one key component was the ability to use its flame gun during amphibious landings. It was clear Project D.30 was being created with an eye to dealing with the Japanese.
One requirement for Project D.30 was the ability to fire hydrocyanic acid instead of lit fuel. Now before you get ideas of dissolving the enemies, or even causing chemical burns, that wasn't the aim. Hydrocyanic acid also has several other names, which will give you an idea of what the aim was. One name is use during the period in other documents is "prussic acid". However the other name for it is this compounds most famous; Zyklon B. Yes, the ability to spray gas at the enemy was still in development as late as 1944. It's common in the 1930's when you see tanks for smoke laying or similar, but the trend seems to fall out of favour after the start of the war.
So what of the effects of a flame thrower? This is of some hot debate in tabletop wargaming circles. In one of my first articles that I wrote a long time ago for World of Tanks EU portal I mentioned a fight between a Crocodile and a Panther. In that article it says that the Crocodile hitting the Panther with its flame gun only immobilised it. I did check after I read it, the word I had in my original draft was "immolated". Obviously the WOT webmaster who edited it didn't know what the word meant and went for the closest word he understood. So yes a flame thrower will kill a tank.
What of dug in troops? Well the British did conduct trials on these, the first was carried out with a Wasp MK.I while the later trial was carried out by a Crocodile. One big difference between the two which may well account for the results was that the Wasp being an earlier version didn't have a nozzle on the end of the gun, the Crocodile did. In both trials enfilading shots on a linear obstacle, such as a slit trench or wall destroyed the position.
The Wasp Mk.I managed to knock out a position from a range of 40-60 yards, if a wet shot is fired first. The Crocodile managed from 80 yards with a single ignited shot. When moving they found it was impossible to hurt a trench if the occupiers kept their heads down. From these tests it was estimated how much fuel would need to be sprayed onto an area to achieve an effective hit or neutralisation.