If you had no sunburn cream, would it work to cover your exposed skin in mud and gunk as a crude way to prevent sunburn? I have never tried it. I have tried using paper tissues on my face as a sun blocker; that didn't work well.
Yes, mud would work to give some protection from the sun, this is in fact exactly what rhinos and hippos do to protect their sensitive skin in the African safari. If I recall correctly mud protects from the sun best while it is still wet, once it has dried it loses much of its protective quality
This could be effective. Anything opaque that blocks the sun's rays from reaching your skin will be effective at preventing sunburn, whether that's a hat, the shade of a tree, or a layer of mud smeared on your skin. Some animals, like pigs or elephants, will cover themselves in dirt or mud as a means of protecting themselves from the sun. I can't say how effective it is compared to proper sunscreen, but it's certainly better than nothing.