If the egg whites are old, is it safe to make Italian meringue?
In short, if they are safe to eat cooked still they are likely safe to eat in a meringue.

There is a higher chance of salmonella on the outside of shell than the inside. 2 Weeks for eggs in the fridge is not very long. To find out a bit about the bacteria actions within the egg, submerge the whole egg fully in 2 cup a measuring cup of water. Make sure there is a couple inches of water above the egg when you first put it in. If the egg stands up, it is not super fresh, but also not spoiled, if it floats then it is not very fresh. If it jumps straight to the top of the water and bobs around, I wouldnt make meringue with it.

As the egg ages and bacteria develops inside, gases are released which will make the egg float. Eggs that float are still edible, but not super fresh and should be cooked more thoroughly. 

This is a rough guide, but it has always served me well, I learned it from dumpster diving.