[Lupin]

Hi and welcome,

Distilled water is ok but it has low GH(General Hardness). Only fish thriving in soft water can live to that. With 10 gallons tank, you will have to stick with a pair of apistogrammas or a small shoal of tetras and pygmy cories. Distilled water is also very expensive as you'll be doing water changes frequently depending on the stocking level of your tank.

 

[Lupin]

Now you'll be experiencing New Tank Syndrome. Pls try to buy a test kit and pure ammonia. There's a sticky on fishless cycling.
The point there is producing stable conditions and bacteria.
Tetras won't last long when introduced in the early stages of a newly setup tank.

 

[Lupin]

They will. Just try to aerate the bucket with an airpump but not too vigorous. And try limiting the food supply for awhile otherwise the ammonia will easily increased thus killing your fish. Better yet, don't feed them until you set up the tank.

 

[Lupin]

Tap water is ok but you need to dechlorinate it in case it has chlorine and other heavy metals.