Two questions

1. The display case with our trophies (stands or stand?) on the far side of the room

2. Literary criticism is like hiring a (construction worker, tour guide, maid, or teacher?) to the literature that you are reading

1. - The display case with our trophies stands on the ar side of the room.

2.-Literary criticism is like hiring a tour guide to the literature that you are reading.

Explanation:

The explanation for the first answer's question is the following. "Stand" is a noun to qualify that an object is raised without moving in a place. However, the stand is used for the first person. While Stands are used for the third person. Both have the same meaning.

The explanation for Literary criticism is: The construction worker would be the writer. The maid would be the writer's assistant, the teacher would be the editor, while the tour guide would be the Literary Critic because it describes the work, providing an opinion based on his perspective and has no effect on the creation of the work. Which differentiates its role from the editor.

stands