I think they made Perrin kill his girl so that they can have the ax / Hammer story ramped up and moved up timeline wise.

I'm okay with most of the changes. Dragon needs to be a man though, because the dragon needs to be able to go crazy. If the dragon can't go crazy then why are we scared of the Dragon? If the dragon can be a girl, and not touch saidin, but sadair, the story gets a lot less interesting, and changes the whole lore of the world.

No nudity in episode 3.

I think Rand and Perrin not being there with Matt for the dagger is so that they can make it there quicker.