Learn Hardcore Japanese: sono kyousitu de nihongo wo osieru tumori desu. - I plan to teach Japanese in that classroom.

この教室 would mean “this classroom” (closer to the speaker or speaker’s side).
あの教室 would mean “that classroom over there” (far from both speaker and listener).

Why is the particle で used after 教室 instead of に?

Particles で and に both can mark locations, but they have different functions:

で marks where an action takes place. Here, teaching happens in the classroom ⇒ 教室で
に marks a point of arrival/existence or destination. E.g., 教室に行く (“go to the classroom”), 教室にいる (“be in the classroom”)

Why is 日本語 marked with を? Isn’t that the subject?

を marks the direct object of a transitive verb. Since 教える (“to teach”) takes a direct object (what you teach), 日本語を教える means “teach Japanese.” The subject (I/we) is omitted because it’s understood from context.

Why is the verb in dictionary form (教える) before つもりです instead of a polite form like 教えます?

The pattern for expressing intention is:
[dictionary form of verb] + つもりです
You cannot attach ます to つもり directly. So even in polite speech, you use dictionary form + つもりです to mean “plan/intend to [verb].”

What does つもりです exactly mean? How is it different from 予定です?

つもりです expresses the speaker’s intention or plan (“I intend to…”). It’s about personal determination.
予定です (lit. “it’s scheduled/planned”) describes something that is officially scheduled or arranged, often by others or more formal plans.
Example:
学校の都合でその日は休校の予定です (It’s scheduled to be a school holiday on that day).

What’s the difference between using つもりです and the plain form つもりだ?

They mean the same thing, but:

つもりです is the polite form.
つもりだ is the plain (casual) form, more common in informal conversation or writing among friends.

How would you change the sentence to say you do not intend to teach Japanese there?

Make the verb negative before つもりです:
その教室で日本語を教えないつもりです。
Or, in casual speech, you can say:
その教室で日本語を教えるつもりはない。

Could you use ～たいです instead of つもりです? What’s the difference?

～たいです expresses desire or want (“I want to teach Japanese…”). It’s more about current desire.
～つもりです expresses intention or plan (“I intend to teach Japanese…”). It’s a firmer statement of future action rather than just a wish.