Neutral Interstellar Helium (NISHe) is almost unaffected at the heliospheric interface with the interstellar medium and freely enters the solar system. It provides some of the best information on the characteristics of the interstellar gas in the Local Interstellar Cloud. The Interstellar Boundary Explorer (IBEX) is the second mission to directly detect NISHe. We present a comparison between recent IBEX NISHe observations and simulations carried out using a well-tested quantitative simulation code. Simulation and observation results compare well for times when measured fluxes are dominated by NISHe (and contributions from other species are small). Differences between simulations and observations indicate a previously undetected secondary population of neutral helium, likely produced by interaction of interstellar helium with plasma in the outer heliosheath. Interstellar neutral parameters are statistically different from previous in situ results obtained mostly from the GAS/Ulysses experiment, but they do agree with the local interstellar flow vector obtained from studies of interstellar absorption: the newly-established flow direction is ecliptic longitude 79.2 deg, latitude -5.1 deg, the velocity is sim 22.8 km/s, and the temperature is 6200 K. These new results imply a markedly lower absolute velocity of the gas and thus significantly lower dynamic pressure on the boundaries of the heliosphere and different orientation of the Hydrogen Deflection Plane compared to prior results from Ulysses. A different orientation of this plane also suggests a new geometry of the interstellar magnetic field and the lower dynamic pressure calls for a compensation by other components of the pressure balance, most likely a higher density of interstellar plasma and strength of interstellar magnetic field.