"One billion was produced" This one is a bit tricky. It depends on the context. If we are debating how many billions, then we might look at one of them as a singular billion. But that would be very unusual. It is far more likely that the writer/speaker is simply leaving out the clearly implied item that was produced in that quantity. "How many widgets were produced? One billion were produced." It is not necessary, or even standard, to repeat the "widgets" in the response, but it is clearly implied.
An example of using it in the singular might by this exchange: "What was the deficit again? One billion was the deficit last year. I expect it will be two billion next year." In each, the word "dollars" is implied, but we don't move to the plural verb (was/were) or noun (billion). Even if we put the implied word back into the sentence, "One billion dollars was produced" - the only time we would use the plural "dollars were" is if we were talking about the printing of a billion pieces of paper with One Dollar on each of them.
The others are so much easier...
Drop the bracketed words and you'll "hear" the correct word easier:
"Huge amounts [of energy] were required"
"Huge areas [of rain forest] were destroyed"
"Most [of the food] were packaged" [should be was]
Most is a bit tricky too, but you consider it either singular or plural depending on what it refers to, whether stated or implied. You used a singular word food - so it's Most food is. If you used a plural word, you would need a plural verb: Most bananas are. Even if the noun is implied, you use the proper verb in context: "How many of the girls went to the dance? Most were there."