I know its the last thing anyone wants to hear, but you are colossally overstocked. Fish 'curving' is linked frequently to high nitrate levels - what are the nitrate levels in your tank? How often do you do water changes, and how much?
I have an oranda and a ranchu. The oranda was pretty depressed in quarantine when I first got him, he just sat on the bottom staring at the back wall of the tank. When I moved him in with the ranchu, it was love at first sight. He seemed nervous of her but fascinated with her, and even now they're always right beside each other, except when she needs some 'alone time' and he steers well clear! They rest in the water either side by side or floating slightly above each other, sometimes they float face to face and it does look like they're discussing some secret fish topics.
I've introduced a third fish to the tank, and while he's trying to be part of the gang, they do freeze him out an awful lot, and just pretend he doesn't exist. Its in their interactions with him that I can see just how bonded the other two are.
I've forgotten since it's been so long since I've gotten a new fish, but how long should I quarantine a new goldfish for?
I've bought from this shop before and they are the most reputable in Ireland I'd say, and their previous fish were in good condition ( sadly two died due to deformities, because I always pick the ones that need the most help!) but I already have two in the tank and I really don't want them to be in any danger whatsoever.
I have a 100L tub, would that do as a quarantine tank?
I've only ever had bad experiences with algae eaters and fancies.
I have two nerites in my tank, they do a reasonably good job keeping it clear of algae, however you don't want it completely clear of it either. Its also better to treat the root cause of it rather than adding another bioload to it.
What you need to so is get a freshwater test kit - the API freshwater master test kit is the best value. If the shop are only testing for nitrite and pH, then most likely your water will appear 'fine' - however ammonia is the most toxic and most likely causing your fish to die.
Read up on cycling a fish tank, and what's involved to get a better understanding of what you're testing for and why - but ultimately you'll need a larger tank.