Spatial diffusion is believed to be the dominant process for the transport of cosmic rays (CRs) in many astrophysical environments. Often the advection by interstellar matter has to be considered as well. Numerical simulations of charged-particle transport in a magnetic field \(\vec{B}=\vec{B}_{0}+\delta\vec{B}''\) with both a homogeneous and a turbulent component are in accordance with a power-law energy dependence of the parallel diffusion coefficient of \(\kappa\sim E^{1/3}\) up to high values of the turbulence level \(|\delta\vec{B}|/|\vec{B}_{0}|\sim 1\,\). Recent studies have pointed out that this result needs careful interpretation, as the energy range in which the simulations are fully diffusive is limited and the cosmic-ray transport can be both nonlinear with respect to spatial variations and even anomalous, i.e. not Gaussian diffusive. Furthermore, according to measurements by the Fermi Large Area Telescope (LAT), there exists a so-called gradient problem that cannot be explained with standard propagation models: the energy spectrum of cosmic-ray protons measured in the inner Galaxy is harder than in the outer Galaxy. Possible solutions comprise a wind structure dominant in the Galactic center region and a spatially varying diffusion tensor. Perpendicular to the Galactic disk Fermi-LAT and eROSITA data revealed giant gamma-ray and X-ray structures, which might be remnants of past activity of the central black hole or of increased starforming activity in the Galactic center region. Also, robust modeling of the gamma-ray emission through processes related to cosmic-ray interactions is crucial to reveal any possible dark-matter signature from the Galactic center region. The focus during Phase 1 of this project is, therefore, on the Galactic center, and the objectives consist in: