"We have a cat and a dog."
Translation:Nous avons un chat et un chien.
Some of them but not all:
-un chien - une chienne
-un lion - une lionne
-un tigre - une tigresse
-un éléphant - une éléphante
-un cheval - une jument
-un coq - une poule
-un dindon - une dinde
-un taureau/boeuf - une vache
-un singe - une guenon
-un cochon - une truie
-une girafe (no masculine)
-un requin (no feminine) -...
It is because some things likes cats and dogs have an actual sex, each of which requires an assigned grammatical gender. Other things, like cars, don't have a sex and are assigned a gender on what seems like an arbitrary basis. There is no car that is literally male or female (except for some figurative and literary purposes etc.) so only one gender is assigned to the noun.
French people very often use "on" instead of "nous" in speech (and increasingly in writing), because conjugation is simpler.
However, "on" requires a 3rd person singular conjugation (like il/elle) and does not have a complete set of attributes (no object pronoun, for example).
Yes, use chat when referring to a male cat or one of unknown gender. If it is known to be female use chatte.
If it is a group of cats which has one known male cat and the rest are female use masculine chat. If all members of a group are female use feminine chatte.
Some French speakers on this board disagree with the previous comment but leaving aside any discussion of poor speech habits, grammar rules that no longer apply (perhaps), political correctness, one thing is for sure; with Duo, when gender is unclear from the context and you use masculine you won't lose a heart. Sometimes in that situation if you use the feminine form you will.
Of course that refers to the context being unclear, not the reader. Confusion on the reader's part about agreement between modifiers, articles, pronouns and nouns etc. doesn't entitle the student to turn everything into masculine.
I think it is time to you to learn a few conjugations, starting with auxiliaries:
avoir (have): j'ai, tu as, il/elle/on a, nous avons, vous avez (polite sing. or plural), ils/elles ont.
être (be): je suis, tu es, il/elle/on est, nous sommes, vous êtes (plite sing. or plural), ils/elles sont.