Barrel Behind The Door has a few bugs to it that should be corrected, note I use the Wiki for rulings and I can't read japanese, so I can't double check wether OCG rulings are worded diffrently on konami's homesite.

1. You can trigger Barrel to effects that would inflict damage to our oponent, which is obviously a bug since the card clearly state you use it when you would take effect damage, the literal wording being: Activate only when a card's effect that would inflict damage to you is activated. Your opponent takes the damage instead.

2. there are 2 cards I have noticed so far, that does not seem to let Barrel activate, one I am 99% sure the first one are correct as the effect starts a chain, the other... im a bit iffy about, as it doesn't say if it starts a chain or not, the first is Volcanic Queens end phase damage effect, is you choose not to tribute you immediatly take the 1000 damage without being able to use Barrel to negate it, this effect is stated to create a chain so you should have the option to chain to it after you chose not to tribute, same happens if you don't have any monters to tribute, instant damage no activation, the other one is Fortune Lady Earth, my oponent had Barrel Behind The Door, and was hit multiple times by Fortune Lady Eart's Level up damage before my Fortune Lady Wind blasted the face down Barrel to kingdom come, and it didn't seem like he could use it. (have replay of the game with the fortune ladies saved if it's needed)

1. You are right, this is a bug.
In current YGOPro, Barrel Behind The Door can be chained to effects that only inflict damage to opponent. (Replay turn 3)
As you pointed out, its TCG text clearly states that it can be chained only to effects that inflict damage to the controller of Barrel Behind The Door.
Its OCG text doesn't say this clearly, but the OCG ruling office has clarified that it works in the same way as TCG.

2. (a) Volcanic Queen
You are misunderstanding how it works. You choose to tribute or take damage during the resolution.

activate chain 1: Volcanic Queen (nothing is done here)
- (opponent cannot activate Barrel Behind The Door since it's not certain you would take damage at this point)
resolve chain 1: Volcanic Queen - tribute or take damage

2. (b) Fortune Lady Earth
I guess your opponent just didn't want to waste a card over 400 damage.
I could activate it without a problem. (Replay turn 3)