Learn Polish: Pies ma nową piłkę. - The dog has a new ball.

The verb mieć (to have) requires its direct object to be in the accusative case. Since the ball is the thing being had, the feminine noun piłka and its adjective nowa must change to their accusative forms.

Why does the adjective nową end in -ą while the noun piłkę ends in -ę?

Even though they are in the same case (feminine accusative), Polish adjectives and nouns use different ending patterns. Feminine adjectives change their ending to -ą, while most feminine nouns change their ending to -ę.

How would this sentence change if the dog did NOT have a new ball?

If you make the sentence negative, the direct object changes from the accusative case to the genitive case. You would say Pies nie ma nowej piłki.

Is the word order strictly Subject-Verb-Object (Pies ma nową piłkę) like in English?

Not strictly. Because the word endings (-ą and -ę) already show what the object is, you could rearrange it to shift emphasis. However, the order used here is the most natural and neutral way to state the fact.