I suppose this may seem harsh, but, IMO, your tank is WAY overstocked. Taking LR out is a bad thing to have to do, and I am not pleased that your LFS sold you something like a shark to that size tank and apparently without checking your water before selling it.
As mentioned, cycle will do nothing for nitrates, and there is no reason whatsoever to add it to an established tank, IMO...if it is properly stocked and established, there shouldn't be ammonia or nitrite present (which would indicate the need for more biological filtration).
Removing LR may very well have caused trouble...you removed biological filtration at the same time you added two more (big) mouths. I would buy your own water test kits, learn about them. Keep a log, test the water often, especially with the type of fish you keep! Unfortunately, there are many out there, and many turn different colors, and it is hard to know what is going on. Do they use drops or powders to test water?
How much, how often, and what do you feed?
I STRONGLY encourage you to return that remora ASAP. Like YESTERDAY. If it is a remora, indeed, it is not a shark at all, but will be BIG and MEAN MEAN MEAN. Will quite possible end up stressing all the other fish to death, if the lunare (aka lunatic) wrasse doesn't do it first, followed by the squirrelfish (another aggressive big eater). You have a lot of active fish in a small tank. I've had experience with remoras in a 40,000g tank, and they were eventually removed from there because they were killing things and attacking the diver (me!)!
How big is the cat shark, and when are you getting a bigger tank?
Definitely water changes (regularly...IMO, at least 15% twice a month, perhaps more). Watch feedings. Trade some things in. Set up a refugium system to export nitrates.