Can artificial sea water be prepared by mixing sea salt with water?
Yes, it is possible though not easy to make artificial seawater by mixing sea salt and fresh water. An interesting example of this happens at the oceanarium in Lisbon, Portugal, which is one of the largest in Europe. After considerable investigation, it was found that the seawater present in massive quantities just outside the building could not be economically filtered, purified and adjusted to attend the surprisingly demanding and delicate needs of the marine organisms to be displayed. The chemical composition of seawater is actually quite complex, varying significantly with the location and time of collection. As with all life, marine life can be very sensitive to small changes in concentration of compounds, not to mention possible biological incompatibilities between the micro- and macrobiota present in seawater from different regions. The solution chosen for the Lisbon Oceanarium was to import some 16.5 metric tons of sea salt monthly from the Red Sea in Israel and mix it with local fresh water in order to replace the tank water. [1] [2] (Couldn't find a reference in English)

Having said that, you really should consult people experienced in setting up seawater aquariums before trying anything yourself. Seawater aquariums have significantly tougher upkeep and maintenance requirements compared to fresh water aquariums; you can't just mix any old cooking sea salt into water, it has to be in the right concentration, and replacement of the tank water has to be more gradual and frequent, not to mention that the salty water will corrode the actual aquarium more quickly. A good aquarium supplies store should be able to better inform you.

Edit: Now I realize you may actually be interested in cultivating shrimp rather than putting them on display. That's a whole different matter, many many times more difficult. You really need to contact some experts in marine cultivation.