Unfortunately, yes. They could be more transparent and utilize more safeguards to prevent the issue to begin with.
It seems so. The church seems to have done a lot in the act of "preserving the good name of the church". There is a pattern of gaslighting and dismissing victims and skipping legal (and moral) requirements in favor of forgiving perpetrators. For example, leaders are instructed to call a hotline when dealing with issues of abuse - and the hotline is to the church law firm presumably so that the church can keep things quiet rather than to care for the victims. The church has punished those who publicly seek to protect children while quickly forgiving and quietly restoring sexually abusive priesthood holders, Look up Sam Young (a former Bishop and leader of the Protect LDS Children movement who was excommunicated for this involvement) and Joseph Bishop (former MTC president who sexually abused sister missionaries in the basement of the Provo MTC, who was barely chastised and even protected by the church) and tell me who the church should listen to and who should be considered for church discipline...
It certainly doesn't do anything to prohibit them. And that's the real problem. There is no supervision or oversight for the ludicrous amounts of adult-child interactions, especially between male leaders and young girls. Most are trustworthy enough, but you don't have to look hard to find bad apples and sickos.
Yes, a thousand times yes. If you don't believe me, google the topic and convince yourself, based on the content and volume of the stories, that I'm wrong. I'll venture that you won't be able to though.
Not intentionally. They have some now famous screw ups and a system that is not designed to recognize and correct mistakes so those things get perpetuated. I hope it will figure things out though and improve in the future.