Is the fatwa permitting the consumption of manufactured foods containing a small percentage of alcohol that does not intoxicate or impair the mind, such as industrial juices and flavorings, correct?

This fatwa is incorrect. Anything that contains a percentage of alcohol is impermissible to consume, because the criterion for prohibition is the presence of an intoxicant, even if in a small quantity that does not intoxicate. This is based on the Prophet's (peace and blessings be upon him) saying: "Whatever intoxicates in large quantities, a small quantity of it is unlawful," and his saying: "Every intoxicant is unlawful, and whatever intoxicates in a large amount, a handful of it is unlawful." An exception to this is when the intoxicating substance transforms into another substance before being added to juices or foods.