해 is the sun While 햇빛 is the sunlight

"햇빛이 뜨거워요." is now accepted. While it is true that 햇빛 means the sunlight, but we sometimes just say the sun for the sunlight, like "We did our best to keep out of the sun."

Also, that the word for sun was 태양. Are they used the same amount?

뜨거워 just means it is hot to the touch so it can go for food or just objects like the sun