The sentence that uses a subjective pronoun correctly is the first one - Laura and I have written an original play for this year's festival.
The second sentence is incorrect because the word him is not subjective, and neither is her in the third sentence, or them in the last one.
2&3 the one with the president and the one with the cat. key word: WOULD
The unstated assumption in this argument is "don´t eat meat" and if you do it "try to make it in small quantities".
Explanation: having a close look at the sentences, this is what is implicitly assumed-"eating large quantities of red meat is unhealthy" (do not consume meat, it can be harmfull for your health); in fact to be truly healthy, a vegetarian diet is preferable to one that includes meat. (if you really want to be healthy and follow a healthy diet, just concume veggies and get rid of meat).
The apothecary gives Romeo a poison that he requested, because he thought Juliet was dead.