We present the statistical properties of Ly{alpha} emission in 586 galaxies at z=4.5-14.2, observed by multiple JWST/NIRSpec spectroscopy projects, including the JADES, GLASS, CEERS, and GO/DDT programs. We obtain Ly{alpha} equivalent width (EW), Ly{alpha} escape fraction, and ionizing photon production efficiency measurements or upper limits for these galaxies, and confirm that the Lya-emitting galaxy fraction decreases toward higher redshifts. We derive Ly{alpha} luminosity functions from z~5 to z~10-14 with the observed Ly{alpha} EW distributions and galaxy UV luminosity functions, and find an ~3dex decrease in number density at L_Ly{alpha}_=10^42^-10^43^erg/s over the redshift range. Notably, this study presents the first constraints on the Ly{alpha} luminosity function at z~8-14. We obtain the neutral hydrogen fractions of x_HI_=0.17_-0.16_^+0.23^, 0.63_-0.28_^+0.18^, 0.79_-0.21_^+0.13^, and 0.88_-0.13_^+0.11^ at z~6, 7, 8-9, and 10-14, respectively, via comparisons of the reionization models developed by seminumerical simulations with 21cmFAST explaining the observations of Ly{alpha}, UV continuum, and Planck electron optical depth. The high x_HI_ values over z~7-14 suggest a late and sharp reionization, with the primary reionization process occurring at z~6-7. Such a late and sharp reionization is not easily explained by either a clumpy intergalactic medium or sources of reionization in a classical faint-galaxy or a bright-galaxy/active galactic nucleus (AGN) scenario, unless a very high escape fraction or AGN duty cycle is assumed at z~6-7.