  We present the magnetic orders and excitations of the distorted kagome
intermetallic magnet TmAgGe. Using neutron single crystal diffraction we
identify the propagation vectors $\bf{k}$ = (1/2 0 0) and $\bf{k}$ = (0 0 0)
and determine the magnetic structures of the zero-field and magnetic
field-induced phases for $H$ along the $a$ and [-1 1 0] crystal directions. We
determine the experimental magnetic field-temperature ($H$, $T$)-phase diagram
and reproduce it by Monte-Carlo simulations of an effective spin exchange
Hamiltonian for one distorted kagome layer. Our model includes a strong axial
single-ion anisotropy and significantly smaller exchange couplings which span
up to the third-nearest neighbours within the layer. Single crystal inelastic
neutron scattering (INS) measurements reveal an almost flat, only weakly
dispersive mode around 7 meV that we use alongside bulk magnetization data to
deduce the crystal-electric field (CEF) scheme for the Tm$^{3+}$ ions. Random
phase approximation (RPA) calculations based on the determined CEF wave
functions of the two lowest quasi-doublets enable an estimation of the
interlayer coupling that is compatible with the experimental INS spectra. No
evidence for low-energy spin waves associated to the magnetic order was found,
which is consistent with the strongly Ising nature of the ground state.
