This is a very common Chinese expression. 太阳从西边出来了 means “the sun is rising in the west”. It is used to describe a very unusual event. Something that one normally would never expect to happen, just like the fact that the sun would rise in the west.

For example when the husband never cooks, and one day he cooks a delicious dinner. Then his wife would say:
哟，今儿太阳从西边出来了？

Or when her son, who never does his homework voluntarily, one day suddenly does them right after dinner:
哇，你还知道做作业？今天太阳可从西边出来了！

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俗语：百闻不如一见，百见不如一干
拼音：bǎi wén bù rú yī jiàn ， bǎi jiàn bù rú yī gàn
翻译：It’s better to see something with your own eyes instead of only hearing about it. And it’s better to do something instead of only seeing it.

I just came across this proverb which I like alot. 闻 means to hear, as you can see, there is an ear (耳) in the character. 不如 means “is not so good as”. So literally translated, the meaning is “Hearing something a hundred times is not so good as seeing it once. And seeing it a hundred times is not so good as doing it once.” So being practical and active is better than staying passive or depending or others.

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俗话：一回生 二回熟
拼音：yī huí shēng èr huí shú
解释：第一次见面还陌生，再见面就已经熟悉了
翻译：First time strangers, second time friends

A six-character proverb about getting to know people. 一回／二回 are the same as 第一次／第二次 meaning first time/ second time. 生 means 陌生 (strange, unfamiliar). 熟 means 熟悉 (familiar). So the first time you meet someone you are still strangers. And the second time you already know that person. Maybe “friends” is not such an exact translation, because the proverb can go on like this: 一回生 二回熟 三回就是朋友. The third time you are friends. And the second time only acquaintances.

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俗话:一心不能二用
拼音：yī xīn bù néng èr yòng
翻译：Don’t multitask

Literally translated this proverb means: “One heart cannot be used twice”, meaning that you cannot put your whole attention on two different activities at the same time, because this way you won’t get any of those two things done. I found several translations online like “A man cannot serve two masters” or “A man cannot whistle and drink at the same time” or “A man cannot spin and reel at the same time”. Well, I think my translation is the easiest to understand, and it also shows that this proverb’s idea is a bit outdated.
Example:

• 小明刚准备边听音乐边写作业时他爸爸就来教训他一心不能二用。
  Ming was just about to listen to music while doing homework when his dad came and scolded him that he can’t focus on his homework while doing something else.

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俗话：不管三七二十一
拼音：bù guǎn sān qī èr shí yī
翻译：regardless of anything, no matter what may happen

You probably never had maths classes in China. When learning the multiplication tables they make it as short as possible. Thus 三七二十一 3 7 21 is the short form for 3×7=21. So it would be “Not caring about 3×7=21″. But what has maths to do with the proverb? Nothing at all now, but there is a little story behind it:
During the warring states period (战国时代) in China (475-221BC) the king of the state of Qi (齐国) told a minister that they didn’t have sufficient soldiers. So this minister reported his calculations to the king: “There are 70,000 families in the capital and I expect three male to show up from each family. This would give us 3×70,000=210,000 new soldiers.” Obviously, this wasn’t realistic to expect 3 male soldiers from each family.
So later this saying was used to describe unrealistic and not thought-out planning, to criticize or mock someone. It’s not so easy to translate it into English. Here are some other possibilities:

• regardless of the situation and consequences
• regardless of right and wrong
• in spite of anything

An example:

• 他们俩又吵架了。这次她不管三七二十一，拿着她的行李就走了。
  They had another argument. This time she didn’t care about anything, just grabbed her bag and left.
• 虽然外面下着大雨，可我不管三七二十一，冲了出去。
  Although it was raining heavily outside, I stormed out in spite of anything.

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成语：十年树木，百年树人
拼音：shí nián shù mù，bǎi nián shù rén
解释：树：培植，培养。比喻培养人才是长久之计。也表示培养人才很不容易。
翻译：It takes 10 years to grow a tree but 100 years to bring up a good man.

I’m not sure were to classify this, because it’s both 成语 and 俗话, so I’ll also add it to the Proverbs. Seems like they are getting more popular anyway.
This phrase is a bit confusing, because you learned that 树 means tree. However in this case 木 is the tree and 树 is a verb, meaning to raise or bring up. Remember that and the proverb will make sense: It takes 10 years to grow a tree but 100 years to bring up a good man. You might wonder that 100 years is a bit exaggerated. This has two reasons: One is because not the exact number is important, but rather that it takes a lot of time and effort. The other reason is that not only a single man is meant, but rather a whole generation.
So in which contexts can you use this? Most likely in education, you should remember that it’s 十年树木，百年树人。

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俗话：不怕一万，只怕万一
拼音：bù pà yī wàn，zhǐ pà wàn yī
翻译：We don’t fear hard work, we just fear failure.

I like this saying a lot. It shows how a slight difference in word order can create a big difference in the word meaning. 一万 is 10000 while 万一 means “what if”, “in case”. So it means that one doesn’t fear 10000, doesn’t mind a lot of hard work, doing something many times to make sure it works out. One only fears that there is a chance it won’t work the expected way. This is an interesting attitude. It will certainly make you more successful in life, as long as you don’t get too obsessed with it.
It also exists as: 不怕一万，就怕万一
Example:

• 考生们疯狂地复习，不怕一万，只怕万一。
  The students are reviewing like crazy. They don’t mind the hard work, they only fear that they won’t pass the exam.

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成语：无风不起浪
拼音：wú fēng bù qǐ làng
解释：比喻事情发生，总有个原因。

“There are no waves without wind”. Quite straightforward this Chengyu. I also put it under proverbs, because it’s rather colloquial and doesn’t have the typical 4 character structure. It means that everything has its causes and nothing would happen out of nowhere without reason.

• 无风不起浪，他今天发脾气，一定有人惹他了。
  There has to be a reason why he is so mad today. Most likely someone annoyed him.

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