It’s been a long time since I was in school but, if I remember my grammar correctly, an explanation of your query would go like this.
In the sentence, “going to Paris is my desire,” the word “going” is a gerund, the noun form of a verb. It is singular, so we use “is” in the sentence quoted. We also have an informal expression using the gerund form in the plural, “goings on,” meaning proceedings or behavior, especially when regarded with disapproval. In that case “goings” has a plural form and we would use a verb in the third person plural, “the goings on were too noisy.”
I think your difficulty might be that, in your example, you put a period between the words “correct” and “you” but it should be a comma, as the first part of the sentence is merely a modifier.
In the entire sentence ”remembering that first impressions are not always correct, you must always have faith in people” the subject of the clause, ”first impressions are not always correct,” is “impressions” and , since it is plural, we use “are.”
“Remembering’’ is a participle here, a verb form used as an adjective, and the entire phrase modifies the subject of the sentence, “you.”