Yes, you can use 不 for all of your examples, but they won't mean the same thing. 不 and 没 both are negatives, but when used in front of most verbs, they give different meanings. 不 tends to indicate what isn't occurring or might not occur in the future while 没 tends to indicate what didn't occur. Let's look at your examples: 天气不错，没下雨。 This means "the weather is nice; it didn't rain." 天气不错，现在不在下雨。 This means "the weather is nice; it's currently not raining." Notice I added a 在 to indicate that it's happening right now. 他没在写信。 This means "he wasn't writing a letter" during the time period that is being referred to. 他不在写信。 This means "he is not writing a letter" right now. 我没在洗头。 This means "I wasn't washing my hair," again referring to a time period that already happened (could be only seconds ago, but still already happened). 我不在洗头。 This means "I'm not washing my hair" right now. Now be aware that there are exceptions! Certain verbs in Chinese can only take one negative or the other, regardless of time you're referring to. For example: 是 (be/is/am/are) can only take 不 as a negative, and 有 (have) can only take 没. Unfortunately, there is no hard and fast rule to help you memorize which verbs are exceptions and which aren't. I hope this helps. Please let me know if you have anymore questions.

Dio, thanks a lot for your explanations!! It really solves my issue, indeed. Because the examples I had given, I had taken them from answers that were meant to express a current action, not something in the past. So even if I had understood that using 不 would also be a possibility, I didn't know why they had used 没. Now I clearly see the nuances! Thanks a million for your time, master Dio.

不： About the usage of 不, I can advance some examples. 1\这不是我的错。It’s not my fault.——“不” means “not”, the phrase 不是 opposes to 是. 2\不开心\不礼貌。Unhappy\impolite——when 不 modify adjective, it works as a negative to that adjective. It means “it’s not + adj.” Beware here. We can also say “没礼貌”. Like what I said above, 没means “don’t have”, so “你这样做很没礼貌” can read directly in Chinese with “what you did has no polite”, which means “your behavior is impolite”. 3\我不想回家。I don’t want to go home. 你不可以把这件事情说出去。You are not allowed to spread out this message. 今天不下雨。It’s not raining today. 他不说话。He didn’t say anything. In this case, 不 emphasizes the meaning of negative, which means “don’t”. Most of time, 不 is used in this way and expresses negative meaning. You can use 不 to modify many types of word, such as verb, adjective, etc. This topic is so broad that I’m not sure whether I have already covered all circumstances. If you meet any circumstance you don’t understand, I’m glad to explain it. : )

Hi Irene, how’s it going? ; ) I agree with ZhangtheGreat. And I’m going to explain the difference between 没 and 不 in another way. 没： In Chinese, I think mostly 没 indicates “don’t have or there is no”. This meaning contains most of circumstance, including your examples. Let’s check some sentences first. 你有女朋友吗？——我 没有 女朋友 I don’t have girlfriend. 这部电影有意思吗？——没有 意思。 There is no interest of this movie. (which means this movie is boring.) As you see, in these two sentences 没 modifies a noun and it means “don’t have the noun” or “there is no the noun”. However, 没 can also modify a verb, which appeared in your examples. 他把书还给你了吗？——他 没 还给我。 你吃早饭了吗？——我 没 吃早饭。 你去过中国吗？——我 没 去过中国。 In these sentences, we use 没 to modify a phrase with verb. Actually, it does indicate a past meaning (like what ZhangtheGreat said), but sometimes we are not supposed to indicate that meaning. Let’s imagine a situation. You are at home with your mom, and your mom is washing her hair. Now your dad is giving you a phone-call and dialogues below happen. “你妈妈在看电视吗？”——“没有，她在洗头。” or “她没在看电视，她在洗头。” In this case, we don’t want to emphasize the tense because we only intend to negate others assumption. Including your examples, “他没在写信” and “我没在洗头” can also respond to a “right now” question. To understand this usage, in my opinion, we can regard the phrase with verb as a noun. When I say “我没吃早饭”, I regard “吃早饭” as something, and with “没” means I don’t have this thing, which functions a negative meaning successfully. Therefore, you need pay attention to the context to determine what does 没 emphasize, the past meaning or the negative meaning.

Yes. It's right.