Learn Italian: I bambini adorano le caramelle.

In Italian, you almost always use a definite article (il, la, i, le, etc.) when talking about a broad category in general. So, 'children in general' is i bambini, and 'candies in general' is le caramelle.

Is the word 'le' in this sentence the direct object pronoun from this lesson?

No, in this sentence le is the plural feminine definite article (meaning 'the') attached to the noun caramelle. The direct object pronoun le (meaning 'them' for feminine things) looks exactly the same, but you will usually see it placed right before a verb.

How would I change this sentence to say 'Children adore them'?

You would replace the feminine plural object le caramelle with the feminine plural pronoun le. Since these pronouns go right before the verb in Italian, the new sentence would be: I bambini le adorano.

What kind of verb is 'adorano'?

It is the 'they' (loro) form of the regular verb adorare (to adore). To make the 'they' form for an -are verb, you drop the -are and add -ano.