The place of the bit isn't depending on the wringles in the lip, but of where the teeth is. The bit should sit so it has a good space around it - to let it move - without getting close to the teeth. It should also be high enough to make the tounge stay in place. Horses, like people, have different lips, and some doesn't get the wrinkles while some gets plenty of them. The bit on the pics loooks to be about right, but not higher.
It does look like the headstall is a size too small with the side pieces adjusted to fit. Especially the brow band, it keeps the neck piece too much forward and is probably uncomfortable for the horse since it's rubbing. Try a bigger one.
The throat latch is too tight already, but I see why that is. With the headstall further back, the throatlatch can be shorter without interfering with the horses throat,and trhat'll help the bridle to stay in place.
You can try to ride with a fly mask to get rid of the flies :)
And if the throatlatch isn't enough after changing browband, you couldd tie a strap rather tightly in front of the cheek, to keep the bridle there. But I think a bigger browband will do the trick.