When a doubler barrel is scored, is it worth any points? and if so, how many; would the doubler barrel also be doubled (i.e. if doublers are worth 1 point, would it double itself to 2 points).
Also, if a doubler/negation barrel is placed into a goal, are all balls and barrels placed on top of the doubler/negation barrel also doubled/negated?
The Doubler Barrel and Negation Barrel hold no point values, they only act as modifiers to the points Scored within the same Goal.
Yes. Please pay careful attention to the following definitions, which can be found in the VEX Gateway Game Manual. (Bolded text added for emphasis)