Learn Russian: Наша соседка скромная и тихая.

In Russian, long-form adjectives like скромная and тихая are generally used to describe permanent, defining characteristics of a person. Short-form adjectives often sound more formal or literary, or they are used to describe a temporary state. Since this sentence describes the neighbor's everyday personality, the long forms are the most natural choice.

Why isn't there a dash (-) between соседка and the adjectives to replace the missing word "is"?

You typically only use a dash to replace the missing "is" when both the subject and the description are nouns (for example, Моя соседка — учительница, meaning "My neighbor is a teacher"). When the description is made up of adjectives like скромная и тихая, no dash is needed.

How would the grammar change if we moved the adjectives before the noun?

It would change from a complete sentence to just a descriptive phrase. Наша соседка скромная и тихая is a full sentence meaning "Our neighbor is modest and quiet." If you put the adjectives before the noun, Наша скромная и тихая соседка just means "Our modest and quiet neighbor..." and you would need to add a verb to finish the thought.

If we were talking about a male neighbor, which words in the sentence would need to change?

Every word would change to its masculine form. The noun changes to сосед, and the pronoun and adjectives must agree with it. The sentence would become Наш сосед скромный и тихий.