How to properly fix these cracks in exterior window sill
I find that a urethane caulk works wonders in cases like this. It bonds like no other caulk I've used, can be had in a huge variety of custom colors, doesn't shrink much, remains very flexible, and is paintable. I'm most familiar with OSI Quad. 

Be warned, it's extremely sticky--you won't get it off your clothes, and you'll have to wear it off your skin. It cures very slowly, so don't expect it to be skinned over after a few minutes like silicone or latex. 

Cut a small opening on the tube and press firmly to inject the caulk deeply into the crack. Use cardboard or a plastic scraper to remove any excess, pressing very firmly to slice the extra caulk off the surface rather than smearing it wide. Ideally you'll be able to apply and tool the caulk in one pass with the tube nozzle, though.