Learn Swedish: Vändningen är fantastisk eftersom allt blir logiskt. - The twist is fantastic because everything becomes logical.

The adjective logiskt describes the pronoun allt (everything). Because allt is a neuter pronoun, the adjective describing it must also take the neuter -t ending.

Is there a hidden att omitted after eftersom, since this lesson is about dropping att?

In standard Swedish, no. Eftersom works on its own and does not take att. However, in casual spoken Swedish, you will sometimes hear people say eftersom att. Stick to just eftersom in your writing!

Does vändningen specifically mean a plot twist?

It translates literally to the turn, coming from the verb att vända (to turn). It is the standard word for a plot twist in a movie or book, but it is also used for any sudden change or turn of events.

Where would the word inte go in the second half of this sentence?

It would go before the verb: eftersom allt inte blir logiskt. Because eftersom starts a subordinate clause, sentence adverbs like inte must be placed before the verb.