"A fish and a dog are swimming."
Translation:Ein Fisch und ein Hund schwimmen.
‘Einen’ is the accusative form of the masculine article, used for direct objects. The nominative form, used for subjects, is the same for neuter and masculine (i.e. ‘ein’). Here both ‘fish’ and ‘dog’ are subjects, they both perform the action of swimming, neither of them is ‘being swum’.
German does not need a helping verb to form the present tense.
sie schwimmen is completely sufficient -- unlike in English, where "they swimming" is not enough and you need a helping verb to say "they are swimming".
This helping verb is a requirement of English grammar, not German.