Reddening, absorption, and decline rate corrections for a complete sample of Type Ia supernovae leading to a fully corrected Hubble diagram to ν<30,000 km s-1

Photometric (BVI) and redshift data corrected for streaming motions are compiled for 111 Branch-normal,'' four 1991T-like, seven 1991bg-like, and two unusual supernovae of Type Ia (SNe Ia). Color excesses E( B - V)(host) of normal SNe Ia, due to the absorption of the host galaxy, are derived by three independent methods, giving excellent agreement leading to the intrinsic colors at maximum of (B - V)(00) = - 0.024 +/- 0.010 and (V - I)(00) - - 0.265 +/- 0.016 if normalized to a common decline rate of Delta m(15) = 1.1. The strong correlation between redshift absolute magnitudes ( based on an arbitrary Hubble constant of H-0 = 60 km s(-1) Mpc(-1)), corrected only for the extrinsic Galactic absorption, and the derived E( B - V)(host) color excesses leads to the well-determined yet abnormal absorption-to-reddening ratios of R-BVI = 3.65 +/- 0.16, 2.65 +/- 0.15, and 1.35 +/- 0.21. Comparison with the canonical Galactic values of 4.1, 3.1, and 1.8 forces the conclusion that the law of interstellar absorption in the path length to the SN in the host galaxy is different from the local Galactic law, a result consistent with earlier conclusions by others. Improved correlations of the fully corrected absolute magnitudes ( on the same arbitrary Hubble constant zero point) with host galaxy morphological type, decline rate, and intrinsic color are derived. We recover the result that SNe Ia in E/S0 galaxies are similar to 0.3 mag fainter than in spiral galaxies for possible reasons discussed in the text. The new decline rate corrections to absolute magnitudes are smaller than those by some authors for reasons explained in the text. The four spectroscopically peculiar 1991T-type SNe are significantly overluminous as compared to Branch-normal SNe Ia. The overluminosity of the seven 1999aa-like SNe is less pronounced. The seven 1991bg types in the sample constitute a separate class of SNe Ia, averaging in B 2 mag fainter than the normal Ia. New Hubble diagrams in B, V, and I are derived out to similar to 30,000 km s(-1) using the fully corrected magnitudes and velocities, corrected for streaming motions. Nine solutions for the intercept magnitudes in these diagrams show extreme stability at the 0.02 mag level using various subsamples of the data for both low and high extinctions in the sample, proving the validity of the corrections for host galaxy absorption. We shall use the same precepts for fully correcting SN magnitudes for the luminosity recalibration of SNe Ia in the forthcoming final review of our Hubble Space Telescope Cepheid-SN experiment for the Hubble constant.