Randall,
Congrats on the new ride! Even new cars will have some level of contamination in the paint. Ideally, you want to remove those before sealing up the paint, but it is not absolutely necessary. I would say it is more important to do prior to polishing for various reasons. You can pretty much use the HGG at any point you wish. It is a synthetic sealant and I think it will probably be a good reload or topper to what you have already applied. You don't have to wait after you apply the HGG to top it with a wax. In my opinion, it is a bad idea to wash with dish soap. I really think it is better to do a strip wash with Adams Shampoo and 2 oz of APC instead or do a normal wash and then an IPA wipedown with 1:1 water to isopropyl alcohol. But that is really only if you want to completely cleanse the paint to start fresh at this time. You can clay the car before you go to polish it in the future or when you want to start fresh with your LSP. Like Adam said check to see if it is bumpy. Best way to do that is after a wash take a ziplock bag and put your hand in it and glide it over the paint. If it is rough then clay.