If you are flying from North America, overnight, you aren't able to get a full night's sleep, and you land at 6:00 AM, I would suggest booking a hotel room for the night before and tell the hotel you'll be checking in at 8:00 AM. That way, you have a place to shower and sleep because you will be exhausted. I tried to see if they'd check me in early but no such luck. Check-in is typically 3:00 pm and some hotels don't let you check in until 5:00 pm. If you're staying at an Airbnb, double check with the host. It sounds like a waste of money if you're not staying at the hotel there overnight, but you're going to be very glad you did.
I agree with the above, don't stay more than 2 nights in Reykjavik. The city is so small that you can "finish" it within an afternoon. South Coast is so beautiful you will want to reserve at least 2 days to really take in the sights. If you're the type of person who likes to take their time exploring a location and not be rushed around like a tour would, then spread that portion of Iceland out.
Spread your Day 6 out over other days. The glacier hike on its own is a total of 3 hours (1 hour to drive + hike to the ice cave, 1 hour to explore the ice cave, 1 hour to hike back and drive back to the pick up point), and there are no washrooms along the way so don't drink too much liquids for that.
Whale watching also took around 3 hours and if you're not used to being on ships/boats/at sea, you might feel seasick and that will take a toll on your body and not something I'd recommend just before an ice cave tour lol
Each of the activities in Day 6 are a lot and I recommend you do 1 of those per day.
October might be a bit early for ice caves anyway, double check with the tour operator what their perspective is. I went in December and it was perfect!