It's too late in the story for Mr Frost to be anything but Jack. Calling him Mr Frost is almost a pantomime wink at the audience.
The secrecy thing is only illogical if you decide to make it so; one sentence from the author could have made up an explicit reason - but why bother? It simply is. And it's one of the least interesting unexplained items in the story.
The self-fulfilling prophesy aspect is - for me - one of those more disappointing aspects of story: it's so much standard fare for prophesies as to be trite or cliche. Like time-travel stories that wrap themselves in a loop where everything happened as it did because of time travel is both cause an effect.
Hmm... I never saw Bod - the boy who had been talking of revenge - as likely to cry over the loss of the men that killed his family. And you're right, death doesn't mean quite the same to Bod as it does to Scarlett. To quote Silas: ‘I am afraid you do Bod an injustice. But you will undoubtedly be happier if you remember none of this. [...]’
This is a story intended to be suitable for younger readers. It is also a story that feels very much like a fairytale. It certainly doesn't feel like "high fantasy" where we might expect The Honour Guard and The Hounds of God to have come with full pedigree as part of a thousand page epic. It's a short relatively sweet fable and I see your expectation for extraneous details as unreasonable in this context.