Is this Gutter install right?
1 - Many people call many metal shapes "drip edge". First of all, there is "drip edge" there. I don't know if that's just a quick drawing you drew, but you should have an overhang out of the roof on a drip edge.
Examples:




The hanger normally goes through the back of the gutter anyway, but not the drip edge. With an actual drip edge, even if installed the same way as shown, the overhang would help out with the water dripping, and you wouldn't have an issue. That being said, it doesn't mean that you will.

2 - It could.

3 - Good for protection.

4 - If the flange was part of the gutter, made from one piece, you cold have a roof mounted hanger, that's best case scenario, but just replacing that edge metal with a drip edge may be the ticket, that is IF you have issues.