Likely culprits, in order of probability:
- Bad SD card (by far the most likely, especially with cheap cards).
- Bad cable or card reader (more common than you might think).
- Something wrong on your computer (many things can go wrong!).
- A bad connection inside the camera.
- Something horribly wrong with the camera's electronics.
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 — see What causes an SD card to go corrupt?
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. If the problem is at a different point in the chain, though, like the USB cable, you may be able to replace that and try again.
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.