I can't find anything related with how and why the Star was created.
I'm most intrested in the aspect of if/why Azura seems so intrested in mortal souls that she (it) created such an artefact?

Ummm Azura made it...not much else is really known but its most likely she made it for an enchanter.

Azura is a Daedric Prince. Like all Deadra, she craves change and she achieves it indirectly by giving her Daedric Artifact, Azura's Star, as a gift to her champion. Different Daedric Princes interest themselves in different things (example : Mehrunes Dagon is interested in destruction) and Azura happens to be pulled in and interested by the concept of trapping, altering and using souls (just like your average enchanter). The star was created by Azura herself, to represent her :

1) Personality
2) Interest
3) Daedric 'mark'.

No one knows exactly how Daedric Princes create their artifacts. Many believe that they are created in Oblivion and 'conjured' into the Mundus by a Daedric Prince's personality and mind.

This is what I wish to know. Is there more lore in how exactly is she intrested in souls, is there anything she wishes to achieve using them? (Dagon wants to achive destruction, but Azura wants what? just to colect souls)

Azura is known to be a 'good-willed' Daedric prince by mortal terms. Her purpose is, as it seems, to free souls from their 'unworthy' bodies (vampires, bandits, marauders, etc) and 'trap' them into soul gems so that they can be put to a better use. Azura's conversation with Oblivion's champion :


I have seen your name, Traveler, and heard it whispered in twilight. I ask a service, which holds promise of fame and reward. Many years ago, five followers slew the vampire Dratik and its kin, but all were infected by the foul creature. Knowing their fate, they sealed themselves up in the vampire's lair. Their suffering weighs heavily on me. Travel to the Gutted Mine. The door will open to you. Bring the peace of death to my followers, and you shall earn my gratitude.
(The Champion located the Gutted Mine and slew all the vampires inside. When the Champion returned, Azura expressed her gratitude by rewarding the Champion with Azura's Star.)
Thank you, mortal. Their spirits are free, and henceforth, above my shrine, five bright candles shall burn forever in memory of their sacrifice. For your service, take this token, that your deeds might be entered in the Book of Fate.


I'll give you a couple of helpful Azura links :

http://www.imperial-library.info/content/azura.

http://www.imperial-library.info/content/invocation-azura

http://www.imperial-library.info/content/azuras-star