Learn Dutch: Ik zoek een bord om de kaars op te zetten. - I am looking for a plate to put the candle on.

This sentence uses an attributive prepositional infinitive, which describes the noun een bord. When an infinitive phrase describes a noun using a preposition (because you put the candle on the plate), Dutch strands the preposition (op) at the end of the clause, right before te + infinitive.

Is op te zetten here from the separable verb opzetten?

No, it is not. While opzetten is a real separable verb (meaning to set up, or to put on a hat), here op is just a standard preposition. The underlying idea is de kaars op het bord zetten (to put the candle on the plate). Because het bord is moved to the front to be described, its preposition op gets left behind in the clause.

Could I say om de kaars erop te zetten to mean "to put the candle on it"?

You would only use erop if you hadn't just mentioned the plate. Since een bord is the noun immediately modified by the om ... te clause, the word er (replacing the noun) is unnecessary and incorrect here. Just leave the preposition op by itself.

What role does om play in this sentence?