  The {\eta} Carinae binary system hosts the most massive stars with the
highest known mass-loss rate. Its dense wind encounters the faster wind
expelled by the companion, dissipating mechanical energy in the shock,
accelerating particles up to relativistic energies and producing high-energy
(HE) {\gamma}-rays. We used the first 7-year data of the Fermi LAT which span
two passages of {\eta} Carinae at periastron. We extracted low and HE light
curves and spectra in different orbital phase bins using the new PASS8
pipeline. We used particle acceleration in hydrodynamic simulations of the
system in a multi-cell geometry and compared the prediction with the
observations. The {\gamma}-ray emission location is compatible with {\eta}
Carinae. Two emission components are distinguished. The low-energy (LE) one
cuts off below 10 GeV and its flux, modulated by the orbital motion, varies by
a factor < 2. Short-term variability occurs at periastron. The HE component
flux varies by a factor 3-4 but differently during the two periastrons. The
variabilities observed at LE and HE during the first half of the observations,
match the prediction of the simulation, assuming a surface magnetic field of
500 G. The HE component and the thermal X-ray emission were weaker than
expected around the second periastron suggesting a modification of the wind
density in the inner wind collision region (WCR). Diffuse shock acceleration in
the WCR provides a convincing match to the observations and new diagnostic
tools to probe the geometry and energetics of the system. Further observations
are required to explain the periastron-to-periastron HE variability and to
associate it firmly with hadronic origin. {\eta} Carinae is a pevatron at
periastron. Its $\nu$ flux can be detected by IceCube after many years of
observations. Orbital modulations of the HE component can be distinguished from
those of photo absorption by CTA.
