I've seen the animations of icy meteorites filling the primordial oceans with (presumably) pure water, but rocks are not naturally 'salty', in a potato crisp sense, and extracted salt is from dried-out deposits originally from seawater. And why Sodium Chloride in particular ?
I assume that when you ask where it all originated from, you don't mean from the big bang, or the supernovae that created the sodium and the chlorine. In that case it originated from the rocky materials that accreted to form the Earth's crust and mantle.
The animations of ice meteorites containing presumably clear water presume too far. I wonder whether any of them would have included visible ice. If we were to extrapolate from such close up views of comments as we have seen so far, they would have approximated to something more like frozen damp mud.
All common sodium salts are soluble in water and so are most chloride salts. Sodium is common in the Earth's crust and although chlorine is a good deal less common it is less inclined to form stable, insoluble compounds than most other common anions. Calcium chloride for example is even more soluble, but in the presence of common levels of carbon dioxide the calcium forms insoluble carbonates. Similar principles apply to most common chemicals in crust, leaving a lot of sodium chloride that does not really precipitate out of the water.
As for the taste of the rocks, any sodium chloride that they might contain would be prone to rinse out quite quickly in geological terms, leaving only such sodium as is trapped in complex structures of silicates and the like, together with calcium, aluminium, and other cations that prevent solubility. So nearly all your chip flavouring has long since slowed down into the sea. More sodium is still on the way of course, but in that form it does not do much for chips, and there is not a lot of remaining chlorine.
As for your mountain, what shape of mountain are you after? I suppose that a Manneken-Pis would be appropriate, but I leave the calculation of its volume to you. At a rough guess, I should say that a 40 km cube would be plausible, But structurally unsound. How about a fairly steep cone, as high as it is wide? If I have not hopelessly lost a few decimal points (and I would not offer a penny of assurance, since I have done no checking of my figures and done most of the fudging in my head) , that should give something vaguely like a cone 64 km high and wide. In practice it would not be a very stable structure either, but visually impressive.
It would not be a very large item in the scheme of things however. Suppose I miraculously created that cone but did not tell you where on the planet to seek it, and I supplied you with a helicopter to go and search for it, how much fuel and time do you suppose it would take you to have a fifty percent chance of finding it?
>the highest mountains on earth are just over 8km high and you say a 64 km cone would be hard to find?<
Well I suppose you might trip over it, but you would have to be in the right place to notice it. It would not be visible from more than a few hundred kilometres in any direction, and given that the great circle circumference of the planet is some 40,000 km, your chances of being where you could notice the peak at all, even if it were snowy white (which I grant is very likely, bearing in mind that it would be snow collared, though hardly snowcapped). It seems to me that if you wished to find that peak in a hurry, you had better have either a good map or very good luck! :-)
As for the critical angle of salt, I think you are thinking of granular salt; what I was thinking of was solid, crystalline sodium chloride. So the angle of repose does not come into it.
I do freely grant of course that my mountain peak would be more than challenging to climb; it would be positively hazardous to be anywhere near the bottom. The rate of creep would be murderous, probably scattering blocks of salt in all directions all the way up to the top of the breathable atmosphere and beyond. But I did want an attractive and simple shape, and a 10 km high cone would be so hard to spot and so unimpressively shaped that if you did finally locate it, you would be sorry that you troubled, wouldn't you?
Do note that "salt" (on average) does cycle from seas to "earth" and back to the seas again with a period of approx 70,000,000 years. One consequence is that generally speaking the seas do not become more salty with time (excluding initial sea formation and removal of fresh water via ice ages.)
The salt cycle involves the ocean, the geosphere and to a very minor extent the atmosphere.
Minerals are leached from rocks through flowing groundwater and surface
erosion. They enter the rivers and from there the ocean where they
accumulate, making sea water salty. They are removed from the water and
enter the sediment by chemical action.
The sediment is used to form new rock which brings the minerals back into the geosphere.
Salt gets into the atmosphere as spray from wind waves. This may be
carried on to land, constituting a minute pathway from sea to land in
the global salt cycle.
Because the salt cycle operates on such large time scales, establishing a static salt budget is of no relevance to oceanography.