I don't have answers for questions 1 and 2, unfortunately. As to question 3, yes, I do think it's a fascinating play and cannot be performed/studied/written about too much. And it is meant as entertainment not historical fact.
As to question 2, I always get confused by Hamlet's age, I always think that he must be about 17 but, as you say, he's actually 30 so my problem is : why is he going to school? Perhaps this will make things clearer : Hamlet's Age - A Puzzle