Learn Swedish: Jag vaknar tidigt på morgonen. - I wake up early in the morning.

The word tidig is an adjective meaning early. Because it is used here to describe the action of the verb vaknar (how you wake up), it acts as an adverb. In Swedish, you typically turn an adjective into an adverb by adding a -t to the end.

Why do we use the definite form morgonen (the morning) instead of just morgon?

In Swedish, when you talk about a habit or something that happens regularly at a certain time of day, you use the preposition på combined with the definite form of the noun. That makes på morgonen the standard way to say in the morning.

Could I use the verb väcker instead of vaknar here?

No, because they have different meanings. Vaknar is used when you wake up on your own. Väcker means to wake someone or something else up. Since you are talking about yourself waking up, vaknar is the correct choice.

If I wanted to emphasize the time by saying early in the morning first, how would the word order change?

If you put the time phrase first, the verb must still come in the second position, which is known as the V2 rule. The sentence would become Tidigt på morgonen vaknar jag. Notice how the subject jag moves after the verb vaknar!