Context. The mechanisms giving rise to diffuse radio emission in galaxy clusters, and in particular their connection with cluster mergers, are still debated. Aims: We seek to explore the internal dynamics of the cluster Abell 545, which has been shown to host a radio halo. Abell 545 is also peculiar for hosting in its center a very bright, red, diffuse intracluster light due to an old, presumably metal-rich stellar population, so bright to be named as "star pile". Methods: Our analysis is mainly based on redshift data for 110 galaxies acquired at the Telescopio Nazionale Galileo. We identify 95 cluster members and analyze the cluster internal dynamics by combining galaxy velocities and positions. We also use both multiband photometric data acquired at the Isaac Newton Telescope and X-ray data from the XMM-Newton Science Archive. Results: We estimate the cluster redshift, ⟨ z ⟩ = 0.1580, a large line-of-sight (LOS) velocity dispersion σV ~ 1200 km s-1, and ICM temperature kTX ~ 8 keV. Our optical and X-ray analyses detect substructures. Optical data reveal three main galaxy clumps (one at the center hosting the peak of X-ray emission; one at NNW, and one at NE); and possibly a fourth clump at South. There is not a dominant galaxy and the four brightest galaxies avoid the cluster core - ≳ 0.4 h70-1 Mpcdistant from the cluster center - and are ≳ 1500 km s-1far from the mean cluster velocity. Two of these brightest galaxies are located in the NNW and NE clumps. The analysis of the X-ray surface brightness distribution provides us evidence of a disturbed dynamical phase: the strong NNW-SSE elongation, a western excess, and a sharp discontinuity in the northern region which is the likely signature of a shock. Located in the star pile region there is the brightest galaxy of the cluster core (CBCG) and a very compact elliptical galaxy, likely a M32-like dwarf. We show that the star pile, which has a previously determined redshift, has a similar redshift to that of the CBCG. Both the star pile and the CBCG are at rest in the cluster rest frame. The elongation of the star pile and its relative position with respect to the CBCG indicate the same direction pointed out by the NE clump. Conclusions: The emerging picture of Abell 545 is that of a massive, M(R < 1.6 h70-1 Mpc) = (1.1-1.8) × 1015 h70-1 M&sun;, very complex cluster with merging occurring along two directions. Abell 545 gives another proof in the favor of the connection between cluster merger and extended, diffuse radio emission. The star pile, likely due to the process of a brightest galaxy forming in the cluster core, is related to the accretion along the NE direction. Abell 545 represents a textbook cluster where to study the simultaneous formation of a galaxy system and its brightest galaxy.