Learn German: Er liest die Zeitung und hört das Radio. - He reads the newspaper and listens to the radio.

The dictionary form of the verb is lesen (to read). It is a strong verb, which means its stem vowel changes in the present tense for the du (you) and er/sie/es (he/she/it) forms. For lesen, the e changes to ie, making it er liest.

Does hört also have a vowel change since it has an umlaut?

No, the dictionary form is hören (to hear or listen). The ö is already part of the base verb, so no vowel change happens here. It just takes the standard -t ending for er (he). The e-to-i or e-to-ie vowel changes only happen to verbs that have an e in their original stem.

Why doesn't the German sentence use a word for 'to' when saying he listens to the radio?

In English, we say 'listen to'. But in German, hören acts directly on the object without a connecting word, much like the English word 'hear'. So you literally say 'he hears the radio' (er hört das Radio).

Since die Zeitung and das Radio are the things being read and listened to, shouldn't their articles change to show they are objects?