Everything from the 4 lessons of this topic on a few pages: the key idea of each lesson, the diagram to remember, the points to learn and the traps examiners set. Read it, cover it, test yourself.
Electrolysis is the decomposition of an ionic compound, when molten or in aqueous solution, by the passage of an electric current. The electrolyte is the liquid that conducts; the anode is the positive electrode and the cathode the negative electrode. In a molten binary compound, positive metal ions are attracted to the cathode and form the metal; negative non-metal ions are attracted to the anode and form the non-metal. Molten lead(II) bromide gives lead at the cathode and bromine at the anode.
Metals always form at the cathode and non-metals at the anode in a molten compound. Remember that opposite charges attract: positive metal ions go to the negative electrode. Also, a solid electrolyte does not conduct; if the question says the compound is solid, nothing happens until it melts.
An aqueous solution also contains H+ and OH− ions from water. At the cathode, the metal forms only if it is less reactive than hydrogen (such as copper or silver); otherwise hydrogen gas forms. At the anode, a halogen forms from a concentrated halide solution; otherwise oxygen gas forms. So concentrated aqueous sodium chloride gives hydrogen at the cathode and chlorine at the anode, and dilute sulfuric acid gives hydrogen and oxygen.
Sodium is never produced at the cathode from an aqueous solution: it is more reactive than hydrogen, so hydrogen gas is released instead. Sodium metal only forms when molten sodium chloride is electrolysed.
In electroplating the object to be plated is the cathode, the plating metal is the anode, and the electrolyte is a solution containing ions of the plating metal. Metal ions gain electrons at the cathode and coat the object, while the anode dissolves to replace them. Metals are electroplated to improve appearance and to resist corrosion. Extended: copper is refined the same way, with an impure copper anode and a pure copper cathode in copper(II) sulfate solution.
The object being plated must be the cathode. Metal ions are positive, so they are attracted to the negative electrode. Connect the object to the positive terminal and it dissolves instead of being coated.
A hydrogen-oxygen fuel cell uses hydrogen and oxygen to produce electricity, with water as the only chemical product. The overall reaction is 2H2 + O2 → 2H2O. Extended: compared with a petrol engine, a fuel-cell vehicle produces no carbon dioxide or other pollutants at the point of use and is more efficient, but hydrogen is difficult to store, is often made using fossil fuels or electricity, and there are few refuelling stations.
"Fuel cells produce no pollution" is not quite right. The vehicle emits only water, but making the hydrogen can release carbon dioxide, for example when it is produced from methane or when the electricity for electrolysis comes from burning fossil fuels. Say "no carbon dioxide at the point of use".