If you crack an egg on a plate, it should remain a domed shape.
They should be tested for freshness, and you should buy organic free-range eggs. If you crack an egg on a plate, it should remain a domed shape. When you crack it, you can also look inside the shell, where a small membrane remains. The smaller the membrane, the fresher the egg.
To separate an egg: with clean hands, crack the egg and let the albumen pass through your fingers into a bowl, retaining the yolk in your palm.
If you are at all concerned about the risks of eating eggs that are not fully cooked when dressing your pasta, I have a few alternatives. One thing you can do is poach egg yolks in a small sieve. Slip the yolks into a small sieve and place it in a pot of simmering water to coddle for a minute, and add it to the pasta. You can also search out pasteurized egg yolks, available in the dairy case of some supermarkets.