  Active Galactic Nuclei (AGN) display complex X-ray spectra which exhibit a
variety of emission and absorption features, that are commonly interpreted as a
combination of i) a relativistically smeared reflection component, resulting
from the irradiation of an accretion disk by a compact hard X-ray source, ii)
one or several warm/ionized absorption components produced by AGN-driven
outflows crossing our line of sight, and iii) a non relativistic reflection
component produced by more distant material. Disentangling these components via
detailed model fitting can thus be used to constrain the black hole spin, the
geometry and characteristics of the accretion flow, as well as of the outflows
and surroundings of the black hole. We investigate how a high throughput high
resolution X-ray spectrometer, such as the Athena X-ray Integral Field Unit
(X-IFU) can be used to this aim, using the state of the art reflection model
Relxill in a lamp post geometrical configuration. We simulate a representative
sample of AGN spectra, including all necessary model complexities, as well as a
range of model parameters going from standard to more extreme values, and
considered X-ray fluxes that are representative of known AGN and Quasars (QSOs)
populations. We also present a method to estimate the systematic errors related
to the uncertainties in the calibration of the X-IFU. In a conservative
setting, in which the reflection component is computed self consistently by the
Relxill model from the pre-set geometry and no iron over abundance, the mean
errors on the spin and height of the irradiating source are <0.05 and ~0.2 Rg.
Similarly the absorber parameters are measured to an accuracy typically less
than ~5%. Extending the simulations to include blue shifted ultra fast
outflows, we show that X-IFU could measure their velocity with statistical
errors <1% even for high redshift objects (abridged).
