I know the phrase “你给我” means "you give me something", but when people say “你给我出去”, do they mean "You cannot keep me here and let me out"? It looks like there are many variations or combinations of the phrase, such as: 你给我小雨点滋润我心窝；你给我滚；你给我听好了；你给我看清楚了；你给我长点记性；你给我好好想想；你给我放明白点；你给我整无语了；etc of which there is nothing like "you give me" implied. So what is the real meaning?
When 给我 is followed by a noun, it means 'give me'
給我一瓶水 = Give me a bottle of water
When 给我 is followed by a verb or verb phrase, it means 'for me'
給我拿一瓶水來 = Bring here a bottle of water for me
Depending on the context and tone of speech [给我 + v] can be a 'request' or a 'demand'
给我滚! = Go away (I demand you)!
给我修改一下好嗎? = Can you fix it for me? (a request)
你 in 你给我 is a pronoun indicating the sentence is directed to 'you'
你給我一瓶水 = you give me a bottle of water
你给我滚! = You, go away (I demand)
你给我修改一下好嗎? = Is it o.k that You fix it for me? (a request)
你给我出去 literally translates to "you get out from me", however, in this type of use, 给我 is usually spoken with a strict/angry/upset tone to emphasize the command - "you, get out", or in English - "You, for god's sake, get out". It can be dropped to soften the tone - "你,出去".
你给我滚 "You, (for god's sake,) roll away from me" - "你滚".
你给我听好了 "You, (for god's sake,) listen carefully" - "你,听好了".
你给我看清楚了 "You, (for god's sake,) have a clear look" - "你,看清楚了".
In this sentence - "你给我小雨点滋润我心窝", 给我 has its normal meaning - "give me/give to me", and can't be dropped to maintain the meaning of the sentence.
3 main usages of 你给我 structure.
1 The same as literal meaning, you give me. We put object after it.
你给我一杯水。 你给我三个苹果。 你给我一瓶可乐。
2 To emphasize order, demand, or request. We put 你给我 at the beginning of a sentence.
你给我站住！ 你给我做下。 你给我走。
We use this structure when the speaker is very angry, impatient.
3 Similar to 把 structure to express negative meaning.
你给我说糊涂了 is similar to 你把我说糊涂了。 你给我气晕了 is similar to 你把我气晕了。
Quote:- "...of which there is nothing like "you give me" implied"
But there is.
You would find "you give me", ("something") implied in all the examples you gave.
In 你给我小雨点滋润我心窝, what is it you want the listener to "give" you?
Translated literally, it says, "You give me some rain to nourish my heart"
In any language this could be taken to mean you want the listener to "give" you some form of affection, understanding, sympathy, love, etc.
In 你给我滚, or similarly, 你给我出去, the former translates literally as "you give me a roll"
Now, if you want someone to get out of the room or your house, etc, you could do it politely or aggressively. Politely would be "Please, or, do you mind leaving the room"?
In Chinese, the word 滚, "to roll", in this context, has a derogatory meaning. Human beings walk, run, in an upright, dignified manner; but to "roll", (perhaps like some animals), means to have your body touching or on the dirty floor in a grovelling posture is therefore degrading / dehumanizing. Thus asking someone to 滚 is to ask that person to not just walk out of here but to do it in a degrading manner. 你给我出去 has similar meaning but with a much lesser degree of debasement. But still it is an impolite command.
So, in this case, 你给我滚, you are asking the listener to "give" away their dignity and "滚 the bloody hell out of your sight"
In 你给我听好了, you are asking the listener to "give you" their undivided attention and listen very carefully to what you have to say, or else.
In 你给我看清楚了, you are asking the listener to metaphorically "give you their eyes", or rather their focused attention and look very carefully at something of importance. It implies that seeing something mistakenly has grave consequences for the "looker".
I don't think I need to "do" all the rest of the examples as by now you should get the drift. But, as others have said, 你给我 has a derogatory implication to it and thus uttered in an irritated, impatient or angry tone. Use it sparingly.
I submit that since language is a function of mental processes expressed through vocalizations, there really isn't that much innate differences between humans of different racial groups when it comes to outward expressions of various emotional, temperamental states.
So, in English you find "Give me" as well, like, "Give me 5", i.e asking for "High 5s", or the favorite of army drill sergeants, "Give me 20", i.e. do 20 push-ups. And, though not actually "give", but in "Lend me your ears" there is the same metaphorical import.