Learn Farsi: کی میرین خونه؟ - When are you going home?

mirin is the spoken, colloquial form of the formal verb miravid (you go / you are going). In everyday conversational Farsi, the second-person plural ending -id is almost always pronounced as -in.

I learned the word for house as "khane". Why is it "khune" here?

In spoken Farsi, the a sound often changes to a u sound when it comes before an n or an m. So, khane becomes khune, just like nan (bread) becomes nun.

Shouldn't there be a preposition like "be" (to) before "khune"?

In formal written Farsi, it would be be khane. However, in spoken Farsi, the preposition be is usually dropped when talking about going to a destination. You simply say the destination without it.

The verb is present tense, but the translation asks about a future plan. Is this common?

Yes! Just like in English, Farsi frequently uses the present continuous tense to talk about definite plans in the near future. You don't need to use the strict future tense for everyday questions like this.