Part 2; please read part 1 first.

The main problem here is that you are mixing singular and plural; a different sound (singular) for different situations (plural). Since we are talking about many sounds, many situations and many emotions, I would suggest expressing it all in the plural:

I would like to have different sounds for different situations in my life, and for different emotions.

I would like living for music.

This is OK, but it's not a common way of saying it. "Living" is the gerund form; it is more commonly used to express something which is real or concrete. "Living" (in this sense) is a more abstract concept, so you normally use the infinitive; "To live". It would therefore be:

"I would like to live for music."

Music helps me to be more productive, and gives me a range of emotions that I couldn't explain with words.

"Music" is singular so you use "gives", the singular form) instead of "give". It gives, they give.

Well done.

Part 1

Music.

You need to break up some (not all) of your sentences a bit more. Using commas is more of an art than a science, and the easiest way to know whether you're using too many is just to read the sentence out loud. If it sounds like "Yesterday I did something {pause} and then I went somewhere {pause} because I didn't want to do something else {pause} but afterwards I went home" then you'll be able to tell that you are using too many commas in a single sentence because you'll hear that it's hard to follow. If you want a more technical explanation of commas in English (but not TOO technical and written in basic English), this article is a good one:

https://en.oxforddictionaries.com/punctuation/comma

In this case I've suggested putting a semi-colon after the first clause, because you are clarifying HOW you felt strange. At that point I would end the sentence.

But I wouldn't lost my time, so I started to study.

I think I understand what you're saying, but you're mixing tenses. "Would not" (wouldn't) is conditional, and would therefore normally be in the future, whereas "lost" is a past tense. Also you wouldn't normally say "lose time" in this context. A train, for example, can "lose time" if it falls behind its timetable, which is different to what you're saying here. In this case the expression you're after is most likely "waste time"; for example, "But I didn't want to waste my time, so..."

I have studied for all the morning, and after that I felt better than before.

1/ "Have studied" would be used if it had some connection with the present; for example "I have studied Italian for a year". (I am still studying it.) Even if you said that at midday and you still had your books open you could say "I have studied..." because it's still connected to the present. But in this case the study that you are referring to was completed that morning, so you use the simple past form of "I studied".

2/ "For all the morning" is not completely wrong, but it sounds awkward and a native speaker would not normally say that. "all morning" or "for the whole morning" would be common ways of saying this.

I was reading a few minutes ago while I was listening to music.

Remember that in most cases you need an article (normally "a") in front of "few". When used in this way it is almost always "a few". I know I went into this in some detail in one of my past corrections but I can't remember whether it was on one of your notebooks or someone else's.

I'm a classical music addicted.

1/ "Classical" is the adjective form used with "music".

2/ "Addicted" is also an adjective, but in this case you need the noun; "addict".

3/ The next clause deals with a separate issue, so it should be in a separate sentence.

Music.

Music helps me to be more productive, and give me a range of emotions that I couldn't explain with words.