The only way to know if eggs have Salmonella is to test the egg for the Salmonella bacteria.
There's no way to tell if the egg has Salmonella by simply looking at it but cooking the eggs all the way usually kills the Salmonella.
Salmonella is also rare in eggs and for the egg to have Salmonella the chicken who laid the egg also has to have Salmonella.
You can eat eggs with blood spots in them.
Eggs with blood spots in them are perfectly safe to eat.
Blood spots in eggs are the remnants of a ruptured blood vessel that occurred during the egg's formation.
Most often, the ruptured vessel forms a tiny speck or dot of blood with a dark red, brown, or even black hue.
If an egg is bad it will float to the top of a bowl of water and if the egg is good then it will sink to the bottom of the bowl of water.
When buying store bought eggs that have been refrigerated before you bought them and brought them home then yes the eggs need refrigeration especially if you're not gonna use them within 1 or 2 days.
However there have been times I've left out eggs on the counter for 5 days before and they were still okay to eat and haven't gone bad.
But if possible always keep the store bought eggs refrigerated when not eating them or using them for cooking etc.
The refrigeration will make the eggs last longer than they would being outside at room temperature.
Farm Fresh eggs usually are okay out of the refrigerator for a few weeks or so but it's always recommended to keep eggs refrigerated.