Learn Polish: Nie martw się, wszystko będzie dobrze. - Do not worry, everything will be fine.

Martw is the imperative (command) form of the verb martwić się (to worry). When telling someone directly to do or not do something, Polish uses this special command form, which frequently drops the typical endings seen in the present tense.

Why is the word się necessary in this sentence?

The verb martwić się is reflexive. If you drop the się, martwić means to cause worry to someone else. By keeping się, it means to worry yourself, which is how Polish expresses the feeling of being worried.

Why does this sentence use dobrze (an adverb) instead of the adjective dobre to say things will be fine?

In Polish, when you describe a general situation, a feeling, or a state of being with the verb być (to be), you must use an adverb rather than an adjective. This is a common trap for English speakers! Because of this rule, we say będzie dobrze (literally it will be well) rather than będzie dobre.

Is będzie functioning as a future-tense helper verb here?

No, it is the main verb here, meaning will be. While you will often see będzie used as a helper verb combined with another verb to form the future tense (like będzie czytać meaning will be reading), in this phrase it stands alone to describe what the future state will be.