What was the first simulation program?

Answer 1

It is uncertain. The Manhattan project during WW2 ran simulations of various portions of the atomic bomb on: the Harvard Mark I and an improvised system of many dozens of IBM punchcard unit record machines, but although these were programmable digital computers they were not electronic computers. In December 1945 through January 1946 a full simulation of Edward Teller's Classical Super hydrogen bomb design was run on ENIAC showing it to be unworkable (this was likely the first simulation run on a programmable electronic digital computer). The purpose of ENIAC was specifically to simulate the firing of newly designed US Army artillery pieces to prepare Firing Tables to be used by soldiers on the battlefield, but it was not used for this purpose until later in 1946.
Long before digital computers existed analog computers were used to run simulations. One of these analog computers was the MIT Differential Analyzer built in 1929, it was fully programmable and could handle a wide variety of problems that could be solved using differential equations. Much of the design of ENIAC including its method of programming was copied from the Differential Analyzer but reimplemented digitally.