Hard water isn't suitable for cardinals or for most tetras and they will be under permanent osmotic stress in alkaline conditions, leading to increased susceptibility to disease, liver and kidney problems and a shorter lifespan. However, there are a few tetras that can deal with harder water so you may want to consider these:

X-ray tetra - Pristella maxillaris
Congo tetra - Phenamogrammus interruptus
Black widow tetra - Gymnocorymbus ternetzi
False penguin tetra - Thayeria boehlkei
Red - eye tetra - Moenkhausia sanctaefilomenae
Glass bloodfin tetra - Prionobrama filigera
Lemon tetra - Hyphessobrycon pulchripinnis

Regarding nitrate remover: it shouldn't be necessary to use this kind of product. With the right stock level and a weekly 25-30% water change nitrate should be well-controlled.

Yes, that will be fine. Bacteria can survive a couple of days in a tank with the filter running, and several hours without running water. Congratulations, and enjoy your fish

If you've recently redosed it's to be expected. check again after 12 hours.

If nitrite is also 0 then yes, at last!

Glad you managed to sort it out

It can happen, especially in cycles that have been difficult, that the nitrite eating bacteria establish quickly and so you see no nitrite. I think this is what's happening here.

Don't use the nitrate-reducing product whilst cycling as it may cause problems. No need to change water unless the nitrate approaches 100ppm. Other than that change close to 100% once you're cycled before adding your first fish.

Good luck!

I suspect he has gill flukes. Treat with Esha GDex or Waterlife Sterazin.

Are they both in the same tank?

As far as I know, All Pond Solutions' own brand tanks and filters are actually SunSun rebrande so the accessories for those should fit. Other than that, if the tubing is a standard size (12/16 or 16/22) then the appropriate Eheim spray bar will fit.

Possibly microsporidia which is a protozoan infection. Use Paraguard to treat.