Resolved questions
我差一点没哭起来

You can translate "I also did not cry" into “我几乎没有哭”, I think this sentence may make sense to you.

" I almost cried" this is correct。
this topic is too hard for a foreigner. Just remember the whole meaning. That's enough.
for more information:[差一点没] is often used as [almost]. you can treat the 4 characters as a adverb. also[差点没].

"没" usually negatives the closest word following it, not a whole sentence. In this sentence, with 哭起来 it is to mean "I didn't cry." Take the "差一点" in to account, if you understand it in this way. "我没哭泣里，差一点哭。"

no reason 的東西 不可能發生 更不可能代代傳承
正所謂 無風不起浪 事出必有因

這個問題 類似於
好高興 = 好不高興
好傷心 = 好不傷心

以 構詞 的角度來分析
是無法自圓其說的

但是 若從語境與語意的角度來分析
這就是 中國語文中 反諷法 的應用
網友不妨自行揣摩揣摩一下
甚麼時候會用肯定表達法 甚麼時候會用否定表達法
如此 解答自然而然瞭然於胸了

Well,the only thing I can tell you is that this "差一点没" sentence doesn't make any sense to anyone.All you can and have to do is put it in your head. Actually,when I saw the sentence,like"我差点没被吓死",I was think of the thing as you do,"What does this sentence means". And I am a native Chinese speaker.So you see,some sentences in Chinese do not make any sense.But people just say it,say it and say it.And eventually it does make the sense.

Your understanding of this sentence is right.
The only thing is the unique expression of Chinese.
You can use this sentence in two case:
1. To express strong emotion."我差一点没哭起来" used to express very strong will of crying but hold tears in the end. It is stronger than "I almost cried".
2. To ridicule or satirize something, which is the last thing to make you cry in this world.
Or, to ridicule or satirize somebody, who has no common sense, and you feel uncomfortable to get along with that person.