Learn Farsi: ما زود به مهمانی نمی‌رویم.

It perfectly follows the rule for the negative present tense: نـ (ne-) + میـ (mi-) + present stem + ending. The verb is to go (raftan), and its present stem is رو (rav). Since the subject is ما (we), we add the personal ending ـیم (-im). Put it all together and you get نمی‌رویم (ne-mi-rav-im).

Why is there a slight visual break between نمی and رویم in the writing?

That gap is called a half-space. In modern Farsi typing, the negative and continuous prefixes (نمیـ and میـ) are usually kept slightly separate from the verb stem so they don't visually run together. It makes the word easier to read, but it is still pronounced smoothly as one continuous word.

Why does زود (early) come before به مهمانی (to the party)?

Farsi generally uses a Subject + Time + Place + Verb word order. ما (we) is the subject, زود (early) acts as the time, به مهمانی (to the party) is the place or destination, and the verb always goes at the very end of the sentence.

Do I always have to use به (to) when talking about going somewhere?

In formal and written Farsi, yes, you use به before the destination. However, in casual everyday speech, Iranians often drop the به completely and would just say the equivalent of 'we do not go party early'.