Learn Farsi: ما سگ و گربه داریم.

While the formal, written pronunciation of و is "va", in spoken conversational Farsi it is almost always pronounced as a short "o" sound when linking words together. So, سگ و گربه is pronounced "sag-o gorbeh".

The English translation says "a dog and a cat," but I don't see a word for "a" in the Farsi sentence. Why not?

In Farsi, a simple singular noun like سگ (dog) can naturally mean "a dog" or refer to dogs in general. You don't need to add the word for "one" (یک) unless you are specifically emphasizing the number.

Does the "and" phrase (سگ و گربه) have to stay together in the sentence?

Yes, the two nouns linked by و act as a single group. Because they are the object of the sentence (the things you have), they stay together and are placed right before the verb داریم (we have).

Can I drop the word ما (we) at the beginning of the sentence?

Absolutely! The verb داریم ends with -یم, which already tells us the subject is "we". Saying سگ و گربه داریم is perfectly natural, and keeping ما at the beginning just adds a little bit of emphasis.