What is the difference between these two sentences, and which one is correct: 1) La gente quiere que haya más agua. 2) La gente quieren que hay más agua.

This question tests the student's knowledge of the use of singular and plural pronouns, as well as the subjunctive. La gente (the people) is singular, so should be followed by a singular verb, as seen in sentence 1. However, it is common for students to fall into the trap and assume that the people should be followed by a plural verb. Therefore, sentence 1 is correct.
In terms of the subjunctive, querer que is always followed by the subjunctive. In sentence 1, quiere que triggers the use of haya, the subjuntive form of haber. However, in sentence 2, this does not happen, and the conjugation of haber is in the present indicative (hay).
Therefore, sentence 1 is the correct one. If the student cannot correctly detect the difference/which one is correct, it shows an underlying lack of understanding of verb clauses, and the use of the subjunctive, which I would be willing to help with, and teach them.