Learn Russian: Кто-нибудь видел свиней?

The word свиней is the direct object of the verb видел (saw), so it requires the Accusative case. Because pigs are living creatures (animate nouns), their plural Accusative form is identical to their Genitive plural form. As you are learning in this lesson, the feminine noun свинья (pig) takes the -ей ending in the Genitive plural, becoming свиней.

Why is the verb видел in the masculine singular form?

The word кто-нибудь (anyone) is based on the question word кто (who). In Russian, кто and its derivative words always act as grammatically masculine singular subjects. Therefore, even if you are speaking to a group of women, you must use the masculine singular past tense verb видел.

Could I use кто-то instead of кто-нибудь here?

You could, but it changes the nuance. Кто-нибудь means 'anyone at all', which is perfect for general questions where you do not know if such a person even exists. Кто-то means a specific 'someone'. If you asked 'Кто-то видел свиней?', it would sound more like 'Someone saw the pigs, didn't they?' rather than a genuine open question.