Learn German: Weißt du, welche Rasse am allerteuersten ist? - Do you know which breed is the very most expensive?

It intensifies the superlative. While am teuersten simply means "the most expensive", adding aller- turns it into "the absolute most expensive" or "the most expensive of all". It is formed by attaching the prefix directly to the superlative form.

I remember the word teuer has a spelling quirk when comparing things. Why is the 'e' kept in allerteuersten?

You are thinking of the comparative form! When saying "more expensive", teuer drops its second e to become teurer. However, in the superlative form (the "most" expensive), that e stays in place, making it am teuersten. Adding aller- to the beginning does not change this rule.

Why is the conjugated verb ist pushed to the very end of the sentence?

The first part of the sentence, Weißt du, is the main clause. The second part is an indirect question starting with the interrogative word welche (which). This acts as a subordinate clause, which always forces its conjugated verb (ist) to the very end.

Can Rasse be used to talk about human "races" as well as animal breeds?