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.
The biggest issue with this is that the first sentence is run-on, you should consider breaking it into smaller sentences, maybe by getting rid of the "and" after describing the mother, replacing it with a period and letting the father get a sentence of his own. Also, you could try "-on how happy the Railway family is. The story also uses detail on how nice the parents are-" something along those lines, just to break the run-on sentence?
This is minor, but at the end "creates a sense of perfection, by describing their house-" the comma before by isn't necessary, and can either be deleted, or you can rephrase like "a sense of perfection. The story does this by describing-"
I hope this helps! <span />
A ghost delivers a supernatural kiss of death
