Just an FYI, the food tour and the walking tours are both excellent. We have done the walking tour on two trips since we had our adult kids with us and they had not done it before. The food tour is great as you get to sample some of the wonderful restaurants in town and of course it is all local food
What peninsula are you staying on? There are several, so without knowing that I can't really answer the rest of your questions.
Yes, the northern lights top make their appearance at times at the end of August, so keep an eye on several aurora apps to see how the odds are for that.
Our trip next month will be our 5th trip to Iceland. We have done both the golden circle and south coast several times. I would do the south coast tour over the GC tour in a heartbeat. Just better scenery and far less crowded. Although, this summer is record tourism numbers, so everything will be busy. The south coast has been totally sold out for lodging through mid September, and the articles that Iceland put out about this were over a month ago. Most people book their lodging and excursions close to a year in advance. So with all that said, expect everywhere around Reykjavik, the GC and the south coast to be very busy.
Honestly, I would probably skip the Golden Circle and do the south coast and Snaefellsness. Day tours for each. That would give you the most variety for a short amount of time.
Sky Lagoon is wonderful, we have done it twice. Don't forget the local pools though. We went to Sundhollin as it was about 2 blocks from our hotel and we loved it. They open early and stay open late, and it is very inexpensive, about $8 US dollars per person. They have lockers, and even a swim suit spinner. Bring your own towel or rent one.