Context. We present Integral Field Unit (IFU) observations with MUSE and deep imaging with FORS of a dwarf galaxy recently formed within the giant collisional HI ring surrounding NGC 5291. This Tidal Dwarf Galaxy (TDG) -like object has the characteristics of typical z = 1−2 gas-rich spiral galaxies: a high gas fraction, a rather turbulent clumpy interstellar medium, the absence of an old stellar population, and a moderate metallicity and star formation efficiency.Aims. The MUSE spectra allow us to determine the physical conditions within the various complex substructures revealed by the deep optical images and to scrutinize the ionization processes at play in this specific medium at unprecedented spatial resolution.Methods. Starburst age, extinction, and metallicity maps of the TDG and the surrounding regions were determined using the strong emission lines Hβ, [OIII], [OI], [NII], Hα, and [SII] combined with empirical diagnostics. Different ionization mechanisms were distinguished using BPT-like diagrams and shock plus photoionization models. Results. In general, the physical conditions within the star-forming regions are homogeneous, in particular with a uniform half-solar oxygen abundance. On small scales, the derived extinction map shows narrow dust lanes. Regions with atypically strong [OI] emission line immediately surround the TDG. The [OI]/ Hα ratio cannot be easily accounted for by the photoionization by young stars or shock models. At greater distances from the main star-foming clumps, a faint diffuse blue continuum emission is observed, both with the deep FORS images and the MUSE data. It does not have a clear counterpart in the UV regime probed by GALEX. A stacked spectrum towards this region does not exhibit any emission line, excluding faint levels of star formation, or stellar absorption lines that might have revealed the presence of old stars. Several hypotheses are discussed for the origin of these intriguing features.