Yes, you can tile a cinderblock wall .... as for all surfaces, be sure it is as smooth as possible, meaning there are no large protrusions and be sure it is totally clean, especially from any oils.
Cinderblock is safe because it doesn't shift or move. You can definitely dress it up nice. ... Consult a tiling expert for any concerns if your wall has been painted or any other coating applied to it.
Backsplashes are rather easy ...be sure to give the mortar at least 24 hours to dry before you put on the grout.