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A very short, isolated question:
No hopes or dreams
In English, it's very clear that this is "neither hopes nor dreams" i.e. there are no hopes, and also no dreams. In Chinese, which word, 和 or 或 (or some other options) can be used to express this mutual inclusiveness?
没有梦和希望
or
没有梦或希望
Neither. 没有梦也没有希望 is the correct form for nor/neither.
和 in 没有梦和X means "having no dreams" and "another full statement" (X).
或 in 没有梦或X means "having no dreams" or "another full statement" (X)
The preferred rendition for disambiguation would be actually be 没梦想、没希望. Please note the pause mark (as opposed to the comma) and the symmetric syllabic structure, in addition to the repetition of 没.
This is in line with other "balanced" repeated structures in modern standard Mandarin Chinese, such as 又…又… and 连…也…
Generally as others stated, negating like this causes ambiguity.
However in this specific case, 梦想和希望 sounds like an idiom-like word to me, they work together as one phrase, like "bread and butter". So at least to me, 没有梦想和希望 means neither
in oral, 没有希望和/或梦想could be the same for understanding. But in some cases which require very strict expression, legal document or scientific papers, for example, 和and或are different
Personally I would rather use 没有梦，也没有希望, since nor can translate to 也没有. Or just use 没有梦，没有希望.
Use negative word with 和 or 或 both means "nothing mentioned are available". In most cases we use 没有……和…….
In most cases we'll use 和 for your example.
和 is used to describe things that share some features in common, like in your example, 梦想 and 希望 are similar in that there both don't exists in that situation. It corresponds to 'both', 'all', 'neither', etc. So it doesn't matter whether the feature is 'negative' or not.
或 is used to describe one of the things to have the feature. It's like 'either' in English.
Furthermore, there is another difference between them. Sometimes 和 emphasizes that the whole owns the feature, not part of it, while 或 means either part has the same property, too.
No hopes or dreams should be 没有希望，也没有梦想 It is referring 'no' to both hopes and dreams. Despite the usage of 'or' in English form, it shouldn't be direct translation to Chinese using 或。
没有梦或希望seemsambiguousto me.