Aims: We explore the relations between physical and orbital properties of planets and properties of their host stars to identify the main observable signatures of the formation and evolution processes of planetary systems. Methods: We used a large sample of FGK dwarf planet-hosting stars with stellar parameters derived in a homogeneous way from the SWEET-Cat database to study the relation between stellar metallicity and position of planets in the period-mass diagram. We then used all the radial-velocity-detected planets orbiting FGK stars to explore the role of planet-disk and planet-planet interaction on the evolution of orbital properties of planets with masses above 1 MJup. Results: Using a large sample of FGK dwarf hosts we show that planets orbiting metal-poor stars have longer periods than those in metal-rich systems. This trend is valid for masses at least from ≈10 M⊕ to ≈4 MJup. Earth-like planets orbiting metal-rich stars always show shorter periods (fewer than 20 days) than those orbiting metal-poor stars. However, in the short-period regime there are a similar number of planets orbiting metal-poor stars. We also found statistically significant evidence that very high mass giants (with a mass higher than 4 MJup) have on average more eccentric orbits than giant planets with lower mass. Finally, we show that the eccentricity of planets with masses higher than 4 MJup tends to be lower for planets with shorter periods. Conclusions: Our results suggest that the planets in the P - MP diagram are evolving differently because of a mechanism that operates over a wide range of planetary masses. This mechanism is stronger or weaker, depending on the metallicity of the respective system. One possibility is that planets in metal-poor disks form farther out from their central star and/or they form later and do not have time to migrate as far as the planets in metal-rich systems. The trends and dependencies obtained for very high mass planetary systems suggest that planet-disk interaction is a very important and orbit-shaping mechanism for planets in the high-mass domain.