Yes, as a former electronics technician, your calculations are correct. The only difference between 20 and 30 amp relays, is that the switch contacts in the 30 amp relay are designed to handle the higher current, without becoming pitted and failing (burning out). So there is no real difference between the two in most situations, but the 30 amp relay will switch high currents reliably for many more relay operations (on/off) than the 20 amp relay, so would be better to use. The only disadvantage is that higher current relays will typically cost slightly more, due to the more exotic materials used in the switch contacts! A 15 or 20 amp fuse will be OK for the standard 60W bulbs, but you should have at least a 20 amp fuse, or possibly a 30 amp fuse, for 100W or higher bulbs. You should also make sure that the inline fuse holder that you use can handle high currents. A 20 or 30 amp rated fuse holder should be used. Don’t use the type, often with clear plastic insulation, for tubular 3AG fuses, which are sometimes used for wiring in low current car accessories, as they won’t handle the heat from high currents going through the fuse to your lights.
In a lot of countries higher wattage bulbs are illegal, so it depends on whether your country tests cars regularly, such as at an annual roadworthy check, as to whether you can run them. Technically, they are illegal here in Australia, too, but I’ve never heard of anyone being booked for having higher wattage bulbs, and I’ve regularly used 90/130W H4 bulbs in my headlights, in cars which have glass headlights. They shouldn’t be used in most late model cars, which have plastic headlights, as the increased UV output of high power bulbs causes yellowing and cloudiness in the clear plastic headlight lens, and may also melt the plastic if the car isn’t moving. Of course, high wattage (100 or 130W) driving light bulbs are legal here in Australia, and are regularly used in driving lights on cars which are frequently used out in country areas. As long as the headlights are adjusted properly, they shouldn’t dazzle people when they are on low beam. I have heard of drivers changing the bulbs to legal, lower wattage ones before annual roadworthy checks, to pass the test, and then re-installing the high power bulbs afterwards… Not that I’d suggest doing anything illegal, you understand!
The wiring from the battery, via a fuse as close to the battery as possible, to the switched contacts in the relay, and from the relay contacts to the headlights, should ideally be as thick as possible, to minimise voltage drop, and keep the voltage at the headlight bulbs as high as possible. Many manufacturers of aftermarket high quality headlight wiring looms use 8 AWG or 10 AWG wire for these wires. Many electronic shops or car audio shops sell this wire, which is often used for wiring up the power for aftermarket high power car audio amplifiers! I think that you mean mm², not m², don’t you? However, based on your question, I’d go for the thickest wiring you mentioned, which is 4mm², and that should be suitable, although even thicker wire would be better. 8 AWG cable is about 7.1mm², and the 4mm² wire is slightly thicker than 12 AWG. AWG is the American Wire Gauge, which is often used to describe wire thickness. It’s often abbreviated to gauge – 8 gauge, or 8G, or sometimes 8#, instead of 8 AWG, for instance. While car accessory places may not have the thicker 8 or 10 AWG wire, electronics suppliers like Radio Shack or Tandy in North America, or Dick Smith Electronics, Jaycar Electronics, or Altronics here in Australia usually will, and many car audio shops or installers will, too. The 2.5mm² wire is suitable for wiring the power to the relay coil, from the headlight switch – that doesn’t carry much current, so thinner wire can be used.