1. Doty fed Bennewitz the false information to discredit him. [Why did Doty feed Bennewitz false info? Maybe "to discredit him" modifies "fed." Thus, adverbial. Compare: "Information to discredit him was sent to the newspapers." In that case, do you think it modifies "information"?]
2. Bennewitz was actually encouraged to believe that he saw real UFOs. [The active form is something like: "Someone encouraged Bennewitz to believe that he saw real UFOs." The passive is what you wrote. According to my books, the infinitive phrase "Bennewitz to believe that he saw UFOs" is STILL analyzed as an object. Books call it a "retained object."]
3. In order to win a proxy war, the CIA had allowed crack cocaine to flood mostly black urban communities during the crack cocaine epidemic.
I'm sure that this is an adverb infinitive because the infinitive 'to win' can be at the beginning or end and it answers why CIA allowed crack cocaine to flood black communities but I don't know what is the function for the infinitive to flood. [I agree with you that "In order to win a proxy war" is adverbial. "Cocaine to flood communities" is, maybe, the object of "allowed." What did the CIA allow?]
4. The false documents seemed to indicate that there was going to be an alien invasion. [I agree with you: "to indicate that ...." is a subjective complement (it refers to "The false documents"). As Matthew Wai reminded us, some books like to use the term "predicate nominative."]