Learn Hardcore Russian: Такой вкусный торт стоит дорого.

Because it modifies торт, which is a masculine noun in the nominative case (the subject). Adjectives in Russian agree with their noun’s gender, number, and case.

Why is торт in the nominative case here?

Торт is the subject of the sentence performing the action “costs.” In Russian, subjects normally appear in the nominative case.

What does the verb стоит mean in this context, and why is it used instead of продаётся or покупается?

Стоит comes from стоить (“to cost”). It expresses price: “to cost [amount].”

продаётся = “is sold”
покупается = “is bought”
Using those would change the meaning from “what the cake costs” to “what happens to the cake (selling/buying).”

Why is дорого in the adverbial form rather than the adjective дорогой?

Дорого is an adverb modifying the verb стоит (“costs expensively” = “costs a lot”).
Дорогой is an adjective and would modify a noun (e.g., дорогой торт = “an expensive cake”).

Why is the word order такой вкусный торт стоит дорого, and not something like торт стоит такой вкусный дорого?

Russian allows flexible word order, but the neutral pattern here is Subject (такой вкусный торт) + Verb (стоит) + Adverb (дорого). Deviating from this typical order can sound awkward or shift the emphasis.

Why is there no equivalent of “a” or “the” before торт?

Russian has no articles. Definiteness or indefiniteness is understood from context rather than marked by words like “a” or “the.”

How would you say “Such delicious cakes cost a lot” (plural)?

Make everything plural:
Такие вкусные торты стоят дорого.