  Cosmic shear is one of the most powerful probes of Dark Energy, targeted by
several current and future galaxy surveys. Lensing shear, however, is only
sampled at the positions of galaxies with measured shapes in the catalog,
making its associated sky window function one of the most complicated amongst
all projected cosmological probes of inhomogeneities, as well as giving rise to
inhomogeneous noise. Partly for this reason, cosmic shear analyses have been
mostly carried out in real-space, making use of correlation functions, as
opposed to Fourier-space power spectra. Since the use of power spectra can
yield complementary information and has numerical advantages over real-space
pipelines, it is important to develop a complete formalism describing the
standard unbiased power spectrum estimators as well as their associated
uncertainties. Building on previous work, this paper contains a study of the
main complications associated with estimating and interpreting shear power
spectra, and presents fast and accurate methods to estimate two key quantities
needed for their practical usage: the noise bias and the Gaussian covariance
matrix, fully accounting for survey geometry, with some of these results also
applicable to other cosmological probes. We demonstrate the performance of
these methods by applying them to the latest public data releases of the Hyper
Suprime-Cam and the Dark Energy Survey collaborations, quantifying the presence
of systematics in our measurements and the validity of the covariance matrix
estimate. We make the resulting power spectra, covariance matrices, null tests
and all associated data necessary for a full cosmological analysis publicly
available.
