The greenish mineral crystals appear to be olivine (Mg, Fe SiO4), which is in the solid solution series of forsterite (Mg SiO4) and fayalite (Fe SiO4) end minerals. These commonly occur in mafic (Mg & Fe rich) igneous rocks that compose ocean sea floor crust.
The roundness and surface smoothness does not look from heated surface mineral fuse character but by common water current or wave action with sand abrasion.
The magnetism is from magnetite, which is common in mafic rocks high in olivine.