Learn Dutch: Nagellak is te duur om vaak te kopen. - Nail polish is too expensive to buy often.

This uses an om ... te (infinitive) clause. In these clauses, the verb phrase (te kopen) always goes at the very end. Any modifiers, like the adverb vaak (often), must be placed between om and the te + verb.

Why isn't there a direct object in the second half, like "om het vaak te kopen"?

When using the te [adjective] om te [verb] structure (too [adjective] to [verb]), Dutch leaves out the object pronoun if it refers back to the main subject (nagellak). It works exactly like English: we say "too expensive to buy", not "too expensive to buy it".

Why doesn't "nagellak" have an article here?

Nagellak is an uncountable mass noun (made of nagel + lak). Because this sentence makes a broad, general statement about nail polish as a whole, it doesn't take an article, just like in English.

Since this lesson is about split topicalization, where is the split noun phrase here?

This specific sentence actually doesn't use split topicalization because nagellak is the complete subject of the verb is, with no quantifier left behind. If you wanted to apply split topicalization to this topic, you could say something like Nagellak heb ik niet veel (Nail polish, I don't have much of).