Learn Russian: Через час мы увидим этих животных.

The word for animal, животное, is a substantivized adjective. This means it functions as a noun but declines exactly like a neuter adjective. Historically, it just meant "a living (thing)." Because it follows adjective rules, its plural takes adjective endings rather than standard noun plural endings like -ы or -и.

Is этих животных in the accusative or genitive case here?

It is in the accusative case because "these animals" is the direct object of the verb увидим (will see). However, because animals are animate (living beings), the accusative plural form matches the genitive plural form. This animacy rule applies to the pronoun этих and the substantivized adjective животных, giving them both the -ых ending.

Why use через час for "in an hour" instead of a preposition like в?

In Russian, to express that an action will happen "in" a certain amount of time from now, you use через followed by the accusative case. If you used в + accusative (в час), it would mean "at one o'clock" rather than a countdown of 60 minutes.

Why is the future tense expressed as увидим rather than будем видеть?