First video is done practically. You could try creating a displacement map using one of the color channels of the girl layer. Place the "projection video" on a new layer, then use a distort > displacement layer effect and a transfer mode to simulate that look. Really depends on how good of displacement layer you create.
In the second video, he's shot over something that is easy to key. From there the keyed layer is placed on top of the stack, the clouds on the bottom, and then another version of him on the bottom. The clouds track matte is then set to "alpha matte" or "luma matte" then either a transfer mode is used or the opacity of the layer is adjusted to restore some of the singers details(probably both were used).
Johnny Cuevas, Editor
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.