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We assemble a large comprehensive sample of 2534 z~2, 3, 4, 5, 6, 7, 8, and 9galaxies lensed by the six clusters from the Hubble Frontier Fields (HFF)program. Making use of the availability of multiple independent magnificationmodels for each of the HFF clusters and alternatively treating one of themodels as the "truth," we show that the median magnification factors from thev4 parametric models are typically reliable to values of 30 to 50, and in onecase to 100. Using the median magnification factor from the latest v4 models,we estimate the UV luminosities of the 2534 lensed z~2-9 galaxies, findingsources as faint as -12.4 mag at z~3 and -12.9 mag at z~7. We explicitlydemonstrate the power of the surface density-magnification relations Sigma(z)vs. mu in the HFF clusters to constrain both distant galaxy properties andcluster lensing properties. Based on the Sigma(z) vs. mu relations, we showthat the median magnification estimates from existing public models must bereliable predictors of the true magnification mu to mu<15 (95% confidence). Wealso use the observed Sigma(z) vs. mu relations to derive constraints on theevolution of the luminosity function faint-end slope from z~7 to z~2, showingthat faint-end slope results can be consistent with blank-field studies if, andonly if, the selection efficiency shows no strong dependence on themagnification factor mu. This can only be the case if very low luminositygalaxies are very small, being unresolved in deep lensing probes.

z~2-9 Galaxies magnified by the Hubble Frontier Field Clusters I: Source Selection and Surface Density-Magnification Constraints from >2500 galaxies