안녕하세요. 1 They are made from helping verb '나다 ' not verb '나다' meaning to 'happen'. *( Auxililary verb in korean language is a little different from europian language so i will say it 'helping' verb' to avoid misunderstanding concept). As a helping verb , '나다' means to completion of a action. 2, I think that '~하고 나서'and '~하고 나면' are a more specified 'after', strictly speaking. ' ~하고 나서' means 'after' and also finishing or completion of action. '~하고 나면 ' means 'after' 'completion of action' and the condition of following sentence. 3 In my opinion , '~하고 나서' is possible to transalte as 'after doing' but '~하고 나면' is a little far from ' doing and then' because in the '하고 나면' sentence , the completed action in first sentence is closely related to and influences on following sentence. I think '~ 고 나면 ' is closer to 'cause and result' relation. 예문은 사전에서 찾아보시기 바랍니다.

-고 나서 and -고 나면 1) Are they simply made from 나다 (to occur, to happen) + -서/-면? Yes, they are. In this case, 나다 is used as an auxiliary verb and shows the act or action of the preceding word(the main verb) has done or has completed, used after a verb, formed with '-고', like '-고 나다'. for example, 일단은 밥을 먹고 나서 이야기 하자. Let's eat first, and then let's talk about it. 샤위를 하고 나니 기분이 상쾌했다. As I took a shower, I felt refreshed. 샤워를 하고 나면 기분이 상쾌하다. I feel refreshed after a shower, . 2) I know the meanings of the conjunctions -서 and -면 are different, but 나서 and 나면 both seem to mean "after..." or "and so". So, how are they different? It is the same to the difference between connective ending '-서'and '-면', as you know. There is no difference between the usages of both. '-서' is used only as a connective ending showing "sequence of act or action", not "cause and reason", and '-면' is used as a connective ending showing "condition" '-고 나서' is contracted to '-고서', in the same way, '-고 나면, is contracted to '-면'. 3) Instead of using the English translation for 하고 나서 as "after doing", could I just think of it as "doing and then"? Same with 가고 나면... can I think of it as "going and then..."? (I know those aren't literal translations.) Yes, maybe. That could be so, but you should consider the context. It depends on the context all the time. "-면" is usually translated to "if...", or "when...", and "-고 나면" is usually translated to "after...", "for..." for example, You'll feel better for a good night's sleep. 하룻밤 자고 나면 몸이 더 나아질 게다. I always feel so tired after I work out. 운동을 하고 나면 늘 피곤해요. When everything has done, and then I will leave here. 모든 일이 끝나고 나면 나는 떠나겠어요.