You should definitely wash the eggs before you cook with them. As you mention, that is de rigueur for Europeans, as it is in America for things like lettuce and potatoes.
You should wash the eggs before opening them. If you cook them in boiling water without opening them (except for the prick at the bottom), I don't see how washing them beforehand would make a difference.
What ? Is this legitimate or are you being funny ?
I'm European and have never washed an egg before cooking it in my life. what is this ? I crack it open and cook it and am still here.
I do wash my tomatoes when I make a salad with raw tomatoes though. And that's mostly to get stuff off since I'd argue my vinegrette would kill all the bacteria.
And washing your potato ? I'm so confused. Don't we all cook potatoes in boiling hot water ?
The incidence rate for salmonella is pretty low either way, but you should definitely wash eggs before cracking them open, for the same reasons you wash your tomatoes.
As for potatoes, no, we don't all cook them by boiling them in water -- many of us bake them, fry them, or use them for making hash browns. This might just be cultural, but I would actually be more inclined to wash them before boiling them, since the reason you wash potatoes is because they have dirt on them, and just as I wouldn't want to toss dirt into my boiling water, I would prefer to clean (or peel) my potatoes before boiling them.
Nope. In fact when I was in cookery school here in the EU, I was told that it is perfectly safe to eat raw egg here, but that in the US this is never advisable.
You can eat raw egg (yolks and whites) in the EU because chickens are inoculated against salmonella. This has absolutely nothing to do with whether or not salmonella is allowed to accumulate and/or incubate on the outside of the shell.