Learn German: Nein, ich kann leider nicht mitkommen. - No, unfortunately I cannot come along.

Because this sentence uses the modal verb kann (can). Just like with wollen (to want) that you are practicing, the conjugated modal verb takes the second position, and the main action verb (mitkommen) is pushed to the very end in its full, unchanged dictionary form.

I thought mitkommen was a separable verb. Why isn't the mit separated here?

When a separable verb is used with a modal verb like können or wollen, it does not split! The modal verb pushes the entire, combined word to the end of the sentence. You only split it if it is the main, conjugated verb in the sentence (like in Ich komme mit).

Why does leider come before nicht here?

In German, adverbs that express an opinion about the whole situation, like leider (unfortunately), typically come before the word nicht. You can think of it just like the English phrase 'unfortunately not' to help remember the order.

The current lesson is about wollen (to want). Why does this sentence use kann (can) instead?

This is a natural response to a question using wollen! If someone asks about your intention (Willst du mitkommen? - Do you want to come along?), you might reply that you cannot. Both können (to be able to) and wollen are modal verbs, so they behave exactly the same way in a sentence.