Can students learn English through songs? How?

Of course, even through video games and movies too

by hearing the words in the songs.

In movies they can read the subtitles, and also in video games they can look for the words the need to know because the game made them curious .

Yes, of course. Songs are linguistic information packed with everything - grammar, intonation, correct pronunciation, native accent and even slangs. But, better if the FL beginners begin with nursery rhymes.  

Songs and rhymes are an important part of learning languages including English.

 

How it works? To understand its phenomenon we need to analyse it.

1- Poetry is more effective way of communication. A stanza can convey a message effectively than a chapter in prose. 

2- Rhythm is something more fascinating for a learner to focus so he learn it fast.

3- Some words with their hard pronunciation in the second language doesn't allow the learner to move his tongue in a certain way. Songs and rhymes resolve this issue beautifully and make the muscles of the learner's tongue more flexible to pronounce such vocabulary perfectly.

Rhymes and songs are taught to the students from elementary level. The repetition and rhythm help students to remember the words and give them confidence of speaking English.

I believe so. In addition to improving their phonetic and speaking skills, songs improve people's use of languauge and figures of speech. This is because a single song revolves around one main theme or idea, and just like poems and ballads songs usually rely heavily on figurative language (similes, metaphors, symbols... etc.) in expressing this idea.