Here are the verb moods for each of the sentences:
-
If the weather improves, we will go to the beach tomorrow.
Verb Mood - Indicative (the first part "if the weather improves" is conditional, but the overall sentence is indicative as it states a fact or possibility about the future) -
Please close the door quietly.
Verb Mood - Imperative (this sentence gives a command or request) -
I have a dentist appointment on Monday.
Verb Mood - Indicative (this sentence states a fact) -
If I were a bird, I would fly across the ocean.
Verb Mood - Subjunctive (the use of "were" indicates a hypothetical situation, and "would fly" indicates a conditional situation)