When they announce a new pope the "Habemus Papam" text says "eminentissimum ac reverendissimum Dominum, Dominum Why is it? Why isn't "eminentissimus ac reverendissimus dominus ?
I would say it's the same reason you see papam instead of papa above. That is, the whole thing is the direct object of habēmus.
In other words, the meaning is "we have a Pope, [we have a] most eminent and reverend…" and so on.
The most important idea is already said by Draconis, but...
In case you are not familiar with declensions, nouns, adjectives and some pronouns in Latin change their ending depending on their grammatical function, in an analogous way as verbs in English end in -ed to signify they are in past tense.
In the example you give—Papam and dominum—, the -m ending means they are in the accusative case, i.e., they are objects to the verb, habemus. What do we have?—A Pope, Mr. Jorge Mario Card. Bergoglio. Eminentissimum and reverendissimum are adjectives modifying dominum, and hence must agree (they are also in accusative case)