Does independent internal audit exist in the reality?

yes of course,but specially check who appoint the I.Auditor.and if I.Auditor is report to same who appoints them then idependence hurts.he must report their to audit committee if any or those charged with governance to seems independent.I.auditors behaviour also matters much.he must show professonal behaviour and be ethical in every situation.in situation of above written envoirnment auditor must documented their findings properly report it and most important thing by which he can exert his influence to implement their finding.commenting and brief discussion to implementation. 

Yes, of course.

Impossible because management does not want to stop his business as well as cycle of the company