Learn Spanish (Latin America): Mis chaquetas son nuevas.

In Spanish, possessive adjectives have to match how many things you are talking about. Because chaquetas is plural (more than one jacket), you must use the plural form mis instead of the singular mi. It does not matter that there is only one owner ('me'), only that there are multiple jackets.

Do words like mis and tus change depending on gender?

No, the words for 'my' (mi/mis), 'your' (tu/tus), and 'his/her/their' (su/sus) only change to match singular or plural nouns. They do not have masculine or feminine forms. You would say mis chaquetas (feminine) and also mis zapatos (masculine). Only nuestro (our) changes for both gender and number.

Why does the word for 'new' end in -as (nuevas)?

Adjectives in Spanish must match the gender and number of the noun they describe. Because chaquetas is a feminine and plural noun, the base adjective nuevo (new) changes to its feminine, plural form: nuevas.

Why do we use son here instead of están?