Likely culprits, in order of probability:
- Bad SD card (by far the most likely).
- Bad cable or card reader.
- A bad connection inside the camera.
- Something horribly wrong with the camera's electronics.
- Something wrong on your computer.
The "bad card" scenario is, unfortunately, the most likely, and in that case the pictures are lost. If it is just the reader or cable, transferring the files again might work — but you've probably already tried that. If you reformat the card, it might work fine, but I sure wouldn't trust it.
Bad cards are a fact of life... I buy only brand-name pro-level cards. They're more expensive (possibly exploitatively so) but I think the extra quality guarantee is worth it.
And, sadly, you can't really fix them after the fact. Blocks of data are damaged or missing, and there's no magical way to undo that. In some cases, you can crop and stitch and color-correct bits of the image back into a coherent image resembling the whole. In your first example, you may be able to save the key part of the image — the kid:
There's a seam running right through the face, though, and I didn't spent much time trying to reconstruct that. If the image is irreplaceable, you might put in that time — otherwise, get a new card and get the child to go down the slide again.