Learn Russian: Я хочу купить это сладкое пирожное.

Пирожное is a substantivized adjective. This means it originally started as an adjective but became a noun over time. Because of its origin, it still takes standard neuter adjective endings when it changes case or number, even though it acts purely as a noun meaning pastry.

If пирожное behaves like an adjective, how do I make it plural?

You use regular plural adjective endings instead of standard noun endings. For example, pastries in the nominative case is пирожные. If you want to say a box of pastries (using the genitive case), it becomes коробка пирожных.

Why are the modifying words это and сладкое in the neuter form?

Even though пирожное is a substantivized adjective, it still has a fixed grammatical gender based on its neuter -ое ending. Any pronouns or normal adjectives describing it, like это and сладкое, must be in the neuter form to match.

What case is the phrase это сладкое пирожное in here?

It is in the accusative case because the pastry is the direct object of the verb купить (to buy). For inanimate neuter words, the accusative form is completely identical to the nominative dictionary form.