So is sodium but it'll burn rapidly if you drop it in water. Salt won't even if it's molten (though it can cause a steam explosion just from the heat).
That depends on the salt and the metal. I saw a presentation by someone from Elysium, who said that chloride salt (which they're using) corrodes stainless steel less than water does. A mix of salt and water is more corrosive, but molten salt by itself is fine.
FLiBe is more corrosive to steel but there are advanced alloys that withstand it fairly well.
Another approach is to use a modular design that makes it easy to replace parts before they corrode too much. Thorcon and Terrestrial Energy use small reactor cores that get replaced every few years.
The open-sourced design uses molten salt, which is the very stable stuff you probably have in a shaker on your kitchen table.