Oooh, a shop that says strips are rubbish instead of trying to sell them to you.
Zero nitrate is unusual unless you've just done a big water change with water that doesn't contain any - and that's unusual in the UK. Some places have 40ppm in the tap water. With nitrate being the end point in the nitrogen cycle, a tank usually has a reading somewhere above zero for that. But nitrate liquid testers are not terribly accurate. If the shop man didn't shake one bottle hard enough, it would have given a false reading.
How do introduce new fish to the tank? The better way is to float the bag in the tank and add small amounts of tank water every 15-ish minutes for a couple of hours to gradually change the bag water to the same as your tank.
Do you have a combi boiler or a hot water cylinder fed by a header tank in the attic? With a combi boiler, it is OK to use hot tap water. With the hot water cylinder, there could be anything in the header tank in the attic, so you should boil a kettle.
Adding a small volume of RO at each water change will lower your hardness, but if it's only a tiny % of the total water change not by much. Be careful about changing the water conditions with RO too much at any one water change.
Melafix is more akin to dettol for us - fine to stop an infection getting in a wound but not much use once an infection has taken hold. Be warned, it smells of tea tree oil!