Learn Farsi: من فکر می‌کنم که این داستان‌ها فقط خرافات هستند. - I think that these stories are only superstitions.

Yes, just like in English, the complementizer که (that) is often dropped in everyday spoken Farsi. However, keeping it helps clearly separate the two clauses (the thinking part and the superstitions part) and is standard in written or slightly more formal Farsi.

Why is این (this) used instead of a plural word for "these", since داستان‌ها (stories) is plural?

In Farsi, demonstrative adjectives like این (this) and آن (that) do not change to plural when they come directly before a noun. You only add the plural marker to the noun itself. So, این داستان‌ها is the grammatically correct way to say "these stories".

The verb هستند (are) is plural. Don't inanimate objects usually take singular verbs in Farsi?

You are right to notice that! Usually, plural inanimate nouns like داستان‌ها (stories) take a singular verb like است (is). However, using the plural verb هستند is also perfectly correct, especially in more formal or written Farsi. In everyday speech, you will likely hear people use the singular form instead.

I know می‌کنم means "I do". How does it mean "I think" here?

It is part of a compound verb. Farsi creates many verbs by combining a noun with a helper verb like کردن (to do). Here, the noun فکر (thought) is paired with it to make فکر کردن (to think). So فکر می‌کنم literally translates to "I do thought".