Question 4 and 5 are both plot twists, not inconsistencies in the series.
Dumbledore wanted as little people as possible to know about it, so as not to alert anybody to the fact that he was doing this. Perhaps as a tactician he was unwise to select Harry, but Dumbledore being the Dumbledore he was, Harry was his most obvious choice. Harry’s deepest desire and personal interest was to destroy Voldemort, and Dumbledore would have known that and respected that, and would have wanted to give him the chance. Dumbledore probably felt that he owed it to Harry to finally explain everything to him, and give him the ultimate chance to sort it out himself.
Harry was the one who would have given up his entire life to destroy Voldemort, and ultimately would be the one who had to give up his life to destroy himself, the Horcrux. It definitely would have saved a lot of mess to arrange him giving himself up rather than trying to trap Harry into falling to Voldemort. Harry coming to the decision himself, after having a full understanding on what Horcruxes were and Voldemorts psych, was the wisest choice.
Finally, there is the Prophecy. The prophecy dictated that it would be Harry who would finish off Voldemort, if anybody would ever. Dumbledore had to try arrange that to the best of his ability.