Learn Spanish (Spain): Mi padre es alto.

No, the word mi (my) is the same for both masculine and feminine nouns. We say mi padre (my father) and mi madre (my mother). It only changes to match number: if you are talking about more than one person or thing, you add an -s to make it mis.

Why do we use es here instead of está?

Es comes from the verb ser (to be). In Spanish, we use ser to talk about core traits and physical descriptions, like being tall (alto). We use the other Spanish verb for to be, estar, for temporary feelings or locations.

Would alto change if the sentence was about my mother instead of my father?

Yes! In Spanish, describing words (adjectives) must match the gender of the person they describe. Because padre is masculine, we use the masculine form alto. If we were talking about a mother (madre), which is feminine, we would change the ending to an -a and say Mi madre es alta.