Can drinking salt water make you throw up? if so how much would you have to drink and how long would it take to make you throw up?

This is a question of curiousity, I see...

Well there is no definitive answer to this, but first let me answer your question on vomit No... Salt can kill you but not in that way. Salt is absorbed into your blood stream however if there is too much salt it lowers the concentration of water in your blood. Now water diffuses across a membrane to areas of higher to lower concentration. The water in cells will diffuse into th blood an you will eventually spill all the water out in your ruin (water is filtered from blood in kidneys). This can make you very. Very. VERY dehydrated. The lower volume of blood can lead to hypovolemic shock. 

Salt can also kill you in the long run by exacerbating or causing hypertension. 

Salt can not kill you if you were to drink it.

Protein helps build muscle and provide energy