Learn Farsi: میرم خونه.

With verbs of motion like رفتن (to go), Farsi speakers frequently drop the preposition به in everyday conversation. You just state the destination directly.

Is it necessary to use the present continuous form دارم میرم to say 'I am going'?

Not always. While دارم میرم emphasizes that you are in the exact middle of the action, the standard present tense میرم is perfectly natural and common for actions happening right now.

Could this sentence also mean 'I will go home'?

Yes. In spoken Farsi, the present tense is routinely used to talk about the near future. Depending on the context, this could easily mean 'I am going to go home' later today.

Why is it written as میرم instead of می‌روم or می‌رم?

In casual writing and texting, the present tense prefix می is often joined directly to the colloquial verb stem without a space or half-space, condensing the formal می‌روم into میرم.