The 2 filters the OP has purchased will not remove the copper and iron from the water assuming they are dissolved and not particulate. Only an RO unit can do that. Standard 2 stage filters (sediment, carbon) remove sediment, bacterial contamination, chlorine and dissolved organic compound. They will not remove dissolved inorganic ions such as copper and iron and any of the brewing related ions (calcium, magnesium, sulfate, chloride).
As for whether either copper and iron will impact on your beer the answer is a definite yes. They will accelerate oxidation. From a chemistry perspective, oxygen can't react with organic compounds, it first reacts with transition metals (due to the electronic configuration of oxygen) and iron and copper are very good at it as they can redox cycle and rapidly activate the oxygen in to a compound that can react with organic compounds.
If you are going to use an RO system make sure you use a good pre-sediment filter and change it regularly.
Rainwater can be great for brewing providing you know what is in it. Bore water is generally very high in dissolved minerals but as a first step, test.