I wanted to ask a few questions about namaz. I was diagnosed of Mixed Anxiety and Depression and I've been having it for over a year now. The medicine I take makes me drowsy and unable to wake up despite having an alarm for Fajr activated. I would like to know what flexibility Islam gives me here, and what do I have to do since I can't get up for Fajr no matter how hard I try.

Secondly, a cause of depression is that one feels without energy throughout the day and sleeps a lot. Due to this I often miss my Zuhr, Asr, Maghrib or Isha. I hardly have any energy because of my disease. What kind of flexibility does Islam give me here?

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You have to try to arrange taking the medicine in a way that allows you to be awake at least before the prayer becomes qaza, so that you can pray on time.
If you are taking the dose at night, then take it early, so that you get enough sleep, and wake up before sunrise.
If despite all the precautions, you still woke up after time, then you just need to pray qaza.