Learn Croatian: Moj otac hoda prema centru. - My father is walking towards the center.

The preposition prema (towards) requires the following noun to take the dative case. For a masculine noun like centar, we add the dative ending -u.

What happened to the letter 'a' in centar when it became centru?

This is a common pattern called the 'fleeting a'. In many masculine nouns, the a in the final syllable drops out when an ending is added. So, centar plus the ending -u becomes centru, not centaru.

Could I say Moj otac hoda k centru instead, using the other preposition from this lesson?

Grammatically, yes, because k (or ka) also means 'towards' and takes the dative case. However, in everyday Croatian, prema is heavily preferred for going towards places or objects, while k is mostly used when going towards a person.

Could I translate 'is walking' as ide here instead of hoda?

You could use ide (is going), but it changes the meaning slightly. Ide just means he is on his way there, which could be by car, bus, or on foot. Hoda specifically emphasizes that he is walking.