If we provide adequate water supply will it be possible to grow plants/seeds/moss/algae (from Earth) on Mars? How different are Mars soil from Earth's soil?
Some of the rocks on Mars aren't too bad for growth of plants or bacteria. They contain a considerable amount of clay minerals (about 20%), and several other minerals which are considered as essential and sufficient for bacteria to survive, at least.
Probable chlorinated salts, e.g. perchlorates, which are likely and wide-spread in Martian soil, don't favour plant growth, but there are also some soils on Earth containing perchlorates. Some plants, and some bacteria can cope with a certain concentration of perchlorates. But it would certainly be better to clean Martian soil from perchlorates before trying to grow plants on it.
Basaltic rocks are wide-spread on Mars. They need some weathering to be suitable for growth of plants.
Solar energetic particles, and galactic cosmic rays are more abundant on Mars than on Earth. That's not optimal for plants, but probably just acceptable. A severe problem is high ultra violet radiation due to a missing ozone layer on Mars. Plants wouldn't survive this uv level without shielding. Hence at least a protection by glass or something similar would be needed.
Carbon dioxide for the respiration of plants is present on Mars, but the atmospheric pressure is too low for water to stay liquid over a sufficiently long period. Hence a pressurized containment would be needed.
Btw.: There is permafrost in some regions on Mars; you just need to warm it, and keep it confined, to get water.
How different are Mars soil from Earth's soil?
Mars has no soil.
Soil has an organic component, which (so far as we know) is lacking in Mars regolith. Actually, the Viking probes may have found signs of organic compounds in the Martian soil, but even until today the results of the experiment are in dispute. Interestingly all Martian landers since, with the notable exception of Phoenix and Curiosity, have been designed to not search for organics.