Very high energy (VHE, E ≥ 100 GeV) astrophysics pioneered the study of non-thermal processes describing cosmic rays (CRs) accelerated by galactic and extragalctic objects. CRs can be investigated by observing the Galactic Center (GC), which hosts many VHE sources and emissions, like for instance the Fermi Bubbles (FBs) found by Fermi-LAT in the GeVs. VHE photons can be used to study the still mysterious Dark Matter (DM). Among the best DM particle candidates are the weakly interacting massive particles (WIMPs), which if massive enough can self-annihilate and emit TeV gamma-rays from dense regions of the Universe. The most promising target to search for DM is the GC. Other ones are DM subhalos, predicted in Milky-Way-like galaxies by cosmological simulations. The High Energy Stereoscopic System (H.E.S.S.), an array of 5 Imaging Atmospheric Cherenkov Telescopes (IACT), observes VHE photons between around 50 GeV and tens of TeV. It can observe the GC region thanks to its ideal position in the southern hemisphere. The future array of IACTs, the Cherenkov Telescope Array, will push the boundary of the sensitivity in the TeV energies. The first part of the thesis introduces fundamental concepts on VHE astrophysics, on H.E.S.S., the supposed nature of DM and the statistical methods used in this work. We describe the log-likelihood-test-statistics (LLRTS) and results from a novel Bayesian neural network framework on the spectral and spatial discrimination of a weak signal in the presence of a non-trivial dominating background. The second part of the thesis focuses on the GC region at VHE. The Inner Galaxy Survey (IGS), a 6-years H.E.S.S. observational dataset of the GC is described in detail. The study of the systematics affecting it and the ongoing effort to build background models from extra-galactic observations and run-wise simulations of the IGS are extensively presented. With the IGS, we search for the low-latitude FBs emission in the region of interest defined by the Fermi analysis. For the first time, the FBs are detected up to ~2 TeV and an integrated significance of 9.2σ. We show observed flux points and upper limits. At 1 TeV, the FBs are measured at ~1.2x10⁻⁹ TeVcm⁻²s⁻¹sr⁻¹. From a joint fit of the Fermi and H.E.S.S. analyses, we could obtain the energy cutoff on the photon spectrum, however more effort to include all the systematics is ongoing. The third part reports new results on DM search. Using the IGS dataset, we derive 95% C.L. observed and expected upper limits on the WIMPs annihilation cross-section (<σv>), with the LLRTS and for several annihilation channels. For the τ⁺ τ⁻ annihilation channel, our limits reach 1.2x10⁻²⁶ cm³s⁻¹ for a DM mass of 0.7 TeV, challenging the expected values for thermal DM. At 1.5 TeV DM mass, we improve the limits of 1.6 with respect to previous H.E.S.S. results. For the tested channels, these are the most constraining limits for TeV DM masses. We also investigate limits uncertainties due to the choice of the DM profile and the systematics. Another search for DM signal is performed towards DM subhalo candidates, the selected unidentified-Fermi-objects (UFOs) in the 3FHL Fermi catalog with no conventional astrophysical counterpart. We derive upper limits on the product between <σv> and the J-factor. The DM UFOs emission is excluded down to ~300 GeV. The reach in term of DM signal sensitivity with the current generation of IACTs in the GC region is investigated using a mock IGS dataset, the state of the art gamma-ray yields for the expected DM photon flux and for the DM distribution in the GC, including baryon feedback and stellar kinematic computations. New limits are derived for model-independent DM searches. The derived sensitivity cannot probe thermal Higgsino DM but excludes thermal Wino and Quintuplet DM. We widely explore how the evaluation of different uncertainties can affect the final results. The sensitivity of our analysis is robust against several sources of uncertainties.