Hi！Your question is very valuable. First if all, 感慨means you have feelings or comments on things and you say it out loud or just think of it in heart. 回顾and反观 both has the basic meaning of looking back. Their difference is 回顾means you look back at the past and think about it. 反观may share the same meaning of "however". Sometimes it means unexpected results. I will give you an example. If student A and student B entered school together, and A had better grade in the beginning. However, in the end of the semester, B gets better grade than A through hardwork. Then, as a teacher, I might say: 反观B，没有A有天赋，但获得了更好的成绩。What I mean is I had observation first, then I had my comoarison. About your second question, 回头去看过去is a common saying just like 回顾. However, 回去看过去may be sci-fi. Because 回头means looking back and 回去means going back. Obviously, most people can do the first one unless you have a time machine. I hope my answer can offer you some help. Have fun learning！

首先，感慨和遗憾没有直接的关系，感慨不包含遗憾的意思，不要误用，比如，你要表达对过去的事感觉有遗憾不要说成”我对过去的事很感慨“，那样是没人会理解成你有遗憾的。 回头，比较口语，要表达文雅些，会用”回首“，所以，回头去看过去，回头看过去，就成了”回首过去“，不需要说”看“，回首往事，不说回首看往事。 回顾：顾是回头看，或转头看，比如，环顾。因此，回顾，就是转回头向后看。 反观：观是仔细看，反观就是反过来仔细看，当然也可以指看过去。 因此你可以说：回首过去，回顾过去，反观过去。这样说比较文雅。当然也可以说： 回头看过去，回过头看过去，回过头来看过去，等等。 遗憾，遗，是留下，憾，是不满足，不满意，失望。 而 感慨，感，有所感触，慨，是感叹。感慨，可以是因为满意而感叹，也可以是因为不满意而感叹，但未必是觉得遗憾。比如，好朋友说成了路人就成了路人，我们感慨人生真是无常，但不表示在我们会因为好失去了朋友而遗憾，我们感慨今天的人友谊的脆弱，却不需要为失去了友谊而遗憾伤心。

谢谢你的回答！

"感慨" emphasizes that you have some strong feelings about past things and you (may) want to make some comments on that. “反观” means you want to compare the past and current, you can only use this word when you already said something about current and have to do a comparison. "回顾" is most like the meaning of "look back", "回顾过去' means look back at the past. 回顾 has another meaning that is "review", you can say 回顾课文，回顾知识.etc 回顾is a formal express of "回头看", but there is a better use of that, I recommend you just use "回看" instead of “回头看”. That is also a formal written language. "回去看过去" and "回头去看过去" are a little strange, I think “回看过去” or "回头看过去" are fairly enough.