Learn Hardcore Spanish (Spain): Mi hermana compra una camisa blanca y unos pantalones cómodos. - My sister buys a white shirt and comfortable trousers.

It’s the present indicative, third person singular of comprar. In context it can mean either “she buys” (habitual) or “she is buying” (right now). Spanish often uses the simple present for actions happening now as well as for habits and near-future plans.

Could I say Mi hermana está comprando instead of Mi hermana compra?

Yes. Está comprando emphasizes that the action is in progress at this very moment. Compra is more neutral and can describe a current, habitual, or scheduled action. Both are correct; choose based on the nuance you want.

Why is there no ella? Why does the subject pronoun get dropped?

Spanish is a “null-subject” language. The verb ending in compra already tells you it’s third person singular, so ella is optional. You could add Ella for emphasis or contrast, but it isn’t required.

Why mi and not mí?

Mi (no accent) is a possessive adjective meaning “my,” as in mi hermana.
Mí (with accent) is a stressed object pronoun used after prepositions, as in para mí or a mí.