I think you can totally ignore such tiny differences of the chinese meaning of "when", 'coz just as you listed in the question, you can see all the translated chinese words of "when" are adv.s express a period of time. So for now, I suggest that you just remember to use "何时" when you want to translate a question sentence led by "when" and use "...的时候" when you wanna say a declarative sentence. Indeed there're quite small differences between those words and pls be rest assured that we can understand what you are expressing even some time you are not translating it very accurate. And I think the most important thing is not to let such inessential barrier bind your step in progressing, and when the time coming, you'll be able to varify your expression very naturally :)

何时, means 什么时候, usually used in writing or formal conversations. 你是何时开始学习中文的？ 在那时, means at that time, in those days, then. 在那时，电脑还不普及。 当时, almost the same as 在那时. 当时，电脑还不普及。it's just the same meaning as the former one. and, you can also use it like this way: 当时，我正在看电视。 当场, means on the spot, at once, instantly. 我当场就回答了她的问题。in some cases, instead of 当场, you can use 当时, the meaning is the same. 我当时就回答了她的问题。 在（当）…的时候, 当…时, they're almost the same: 在（当）我吃饭的时侯，开始下雨了。// 当我听到这首歌时，我就会想起他。 在…期间, means during, usually a relatively long period. 在校期间，伊丽莎白同学表现良好。// 在我住在香港的期间，我认识了很多中国朋友。

何时,什么时候 question 那时, then 其时, very old usage, no one use it any more. 在...时, 当....的时候 even in english, these two experssions are very similar. So just suck it up... 在...期间, during

想回到过去when我们在一起 当…时 is the right combination for this statement. 回 想到过去(当)我们在一起(的時候)

Hi, 伊丽莎白，when just express time，it could be point or period. Just try “时候”when you want to translate。 想回到过去，我们在一起的时候. If you just translate a declarative sentence. 想回到过去，那时我们在一起. If you just translate a sentence in a romantic article or poem. Hope could help you.