Hi,

  1) In the sentence: " I love listen to musics", I suppose it's wrong to say this, isn't it?  Yes, it's wrong. The correct should be: "I love listen to music" Yes or "I love listen to songs", no? 'Music' does not necessarily involve a song. And by the way there isn't plural form for the word 'music', isn't it?; Not really.

2) "For different ages, there's a special music" (here I suppose the correct form is: "for different ages, there's a special song", because music refers to the style: rock, heavy metal, opera, while song is the music itself . Am I wrong?     As I said above, 'music' does not necessarily involve singing.

3) "We all here appreciate Pink Floyd and Evanescence's music." (here I suppose the correct is: We all here appreciate Pink Floyd and Evanescence songs, without apostrophe's use . Or can I write ...Evanescence music?)   

These are all acceptable.

Pink Floyd and Evanescence's music

Pink Floyd's and Evanescence's music

the music of Pink Floyd and Evanescence

4) "They study hard at university." (I suppose it is : They study hard at the university); Omit the 'the', unless you are referring to a specific university (eg If you are referring to a specific building, you'd say 'He works in the University that is beside the Church.')

5) When we know very well all the tasks(routine)of a job area, may we say: I know the duties of my area very well.  (?)  I suggest 'I know my job responsibilities very well' or better, 'I am very familar with my job responsibilities'.

Best wishes, Clive

"I love to listen to music" "I love to listen to songs"

And by the way there isn't plural form for the word 'music', isn't it?; Uncountable nouns can't be used in situations where a plural would be used. Some English words are the same for both singular and plural e.g. deer

4: "They study hard at university" - This is a regional sentence. In America, we would say "They study hard at college." In England, the original sentence would be correct.