Questions & Answers about Мы видели семь гусей.
Why is the word for "geese" ending in -ей here?
It's in the Genitive plural case because it follows the number семь (seven). The dictionary form is гусь (goose), which ends in a soft sign (-ь). To make the Genitive plural for nouns ending in -ь, you drop the soft sign and add -ей.
Is гусь a masculine or feminine noun, and does that change how we form the Genitive plural?
гусь is masculine. However, for the Genitive plural, the gender of nouns ending in a soft sign (-ь) doesn't actually matter! Both masculine and feminine nouns that end in -ь take the exact same -ей ending.
The verb видели (saw) requires the Accusative case. Why are we using Genitive rules here?
You are right that видели takes an Accusative object. In this sentence, the number семь is what takes the Accusative case (which looks identical to its dictionary form). But the rule for numbers 5 and higher is that they always force the noun following them into the Genitive plural, regardless of what case the verb wants.
Shouldn't animate objects like geese make the number change its form in the Accusative case?
That's an excellent question, because animate objects do change the rules for numbers 2, 3, and 4. But for numbers 5 and higher (like семь), Russian usually keeps things simple. In the Accusative case, the number stays in its basic dictionary form even when you are talking about living things (animate objects).