We had a full group on my October trip a few years ago, it's a popular trip. The weather was great, hardly ever needed a jacket. I swam in the Med in Antalya and I don't like cold water.
You have to remove your shoes for the mosque visit and we were asked to remove our shoes at the home-hosted lunch, so that was only twice on the entire trip. Sandals are fine, some people on our trip wore them; I think I used lace-ups for some sites where we'd be walking through dirt and a sneaker-type slide that is easy to take off for others. I don't think you need hiking shoes, but might want socks for the mosque and the lunch.
We had good weather and I even swam in the Med in Antalya and I don't like cold water. I think the sea was warmer than the hotel pool.
It was a great trip, one of my favorites, but there are some long bus rides. That didn't bother me, I thought the scenery and the destinations were interesting, but some people complained, which I don't understand because it is clear in the itinerary that there would be long bus rides. There is a map on this web site that clearly shows that there will be a lot of area traveled.
Turkish Air is fine, as good or better than some American airlines. I don't know about their premium economy, I've only used it on Delta and was glad that I did for the extra leg room.
The hot air balloon ride in Cappadoccia is wonderful. I hope you're taking extra days in Istanbul, it's amazing; I yearn to return.