Learn Polish: Lekarz zaczyna patrzeć na wyniki. - The doctor is starting to look at the results.

In Polish, the verb patrzeć (to look) specifically pairs with the preposition na to mean "to look at." When used this way, na must always be followed by the Accusative case.

Is wyniki in the Accusative case here? It looks like the Nominative plural.

Yes, it is in the Accusative case because it follows patrzeć na. The singular noun is wynik (result), which is masculine inanimate. For masculine inanimate nouns, the plural Accusative form is identical to the plural Nominative form, so it stays wyniki.

Why is the second verb patrzeć in the infinitive?

Just like in English when you say "starts to look", only the first verb is conjugated to match the subject (Lekarz zaczyna). The second verb stays in its basic dictionary form, the infinitive (patrzeć).

Could we use a perfective verb for "starting" here instead?

Not in this exact sentence. The action is happening right now in the present tense ("is starting"). Perfective verbs focus on completion and cannot be used in the present tense, so we must use the conjugated imperfective verb zaczyna.