I would like to respond to your sentences (1) and (2).
(A) They all thought he was dead.
(B) They all thought him dead.
The difference is that sentence A is correct but not sentence B. I am guessing that you used “him” in sentence B as an object pronoun because you may have often come across sentences such as: (C) “She misses him.” (D) “She thinks of him.” (E) She wanted him dead.” And yes, the use of “him” in sentences C, D and E is correct. So when should we use object pronouns?
In sentence C, the man is the object (receiver) of the woman’s thoughts (you can also think of the man as the “done-to” of the verb (misses) in the sentence), so the object pronoun (him) should be used. “She misses him.” (correct) / “She misses he.” (wrong)
In sentence D, an object pronoun is used because object pronouns come after a preposition. “She thinks of him.” (correct) / “She thinks of he.” (wrong).
In sentence E, again, the man is the receiver of the verb (wanted), so we use an object pronoun (him).
Sentence B is wrong because “thought” is a stative verb (verbs that describe a state, such as mental processes or emotions, rather than an action. Therefore, we cannot use “him” as an object because there is no action verb in the first place. Sentence A is correct because “They all thought” about something which they believed, and in this case, the something is “he was dead”.
Final example: Think (another stative verb)
I think he is done. (correct. “he” is used as a subject pronoun for the verb “is”.)
I think him done. (wrong.)
I hope this helps.