Learn Hardcore Arabic (Modern Standard): في الصباح آخذ الدواء أيضا، ولا أذهب إلى العمل لأنني متعب. - In the morning I also take the medicine, and I don’t go to work because I am tired.

Arabic often front-loads time/place phrases for emphasis or flow. في الصباح (In the morning) sets the scene first, and the subject أنا (I) is understood from the verb آخذُ (1st person singular). You can add أنا for emphasis: في الصباح أنا آخذُ الدواء أيضًا... but it’s usually unnecessary.

What exactly does آخذُ mean, and why is it spelled with آ?

آخذُ means I take. It’s the present tense (imperfect) 1st person singular of the verb أخذَ (to take).
It begins with آ (alif madda) because the underlying form historically combines a hamza + long vowel sound at the start, yielding the written آ.

Is آخذُ الدواء the most natural way to say “I take the medicine” in MSA?

It’s correct, but many speakers/writers often prefer أتناولُ الدواء (I take/consume the medicine, i.e., take medication) because it clearly implies taking medicine.
So both are fine:

آخذُ الدواء = I take the medicine
أتناولُ الدواء = I take the medicine (more “medication-taking” nuance)

Why is الدواء definite (the medicine)? Can it be indefinite?