So, my teacher said that, by law, you can only use 30 seconds of a scene from a tv show episode. My question is, what if you want to use 30 seconds from episode 1 of a show and 30 seconds of episode 20 of the same show? It's owned by the same people, sure, but it's not the exact same product. Anybody know for sure?

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Your teacher is mis-informed. First, just about ANY use for school has a statutory exemption under the US Federal Copyright statutes (See, e.g., Section 110). Second, there is no general rule about how much of something you can use (outside of the exemptions) without triggering "infringement." There is a famous case of a song by The Beatles in which a single chord was deemed sufficiently creative, recognizable and copied that its use alone was a copyright infringement (first chord of Hard Days Night). It is simply untrue that you can use "30 seconds" of anything and avoid being sued, although the economics of finding you and suing you do tend to focus upon bigger fish.