Hello and some fish behavior questions!

Hiya! Welcome to the hobby!
First, you're going to enter the land of cycling tanks (unless the filter was established, and placed on your tank immediately) which will require you to do a lot of work for the first bit until the cycle settles. There is LOTS of info on the AC site and this forum on cycling, so I won't bore you with the details
If you haven't got test kits, I highly recommend purchasing something like the Tetra 'MiniMaster test kit', or at least Ammonia (NH3), Nitrite (NO2) and Nitrate (NO3). You'll need to monitor these levels DAILY until the cycle's done (at least two or three weeks).
While the tank is cycling, you're going to need to do water changes of 25% to 50% at least every other day to keep the levels of poisonous ammonia and nitrite down - cardinals especially are quite sensitive, and might not make it through the cycle.
That said, IME, fish don't know where they're 'supposed' to stay, lol. I have 'midwater' fish that eat off the bottom, 'topdwellers' who refuse to eat off the surface, and bottom feeders who turn upsidedown to eat off the surface. Fish have personalities and preferences just like us, it seems, and pretty much do what they like!
A fish wandering out on its own (as long as it's not hiding and pale, in which case it's probably not feeling well) isn't a bad thing - mine go on little expeditions and then rejoin the group all the time. If they're secure in their environment and don't fear predation, they'll feel free to leave the group if something takes their interest. Nothing to worry about.
Oh - I'd turn your filter back up, you want it turning over as much water as possible right now to feed and oxygenate the bacteria growing on the filter media.
Enjoy your new tank!

The last post said it all. I'd just add, that its generally a good sign when your minnows aren't schooling tightly and individuals wander off for an adventure--it means they feel safe in the environment. When something new or bad happens in my tank my white clouds form right up in a tight school and none wander off. But slowly they go back to a more spread out happy "school".

Right now I have 2 white clouds lower than my cory cats (who are buzzing around in their night-time ritual). But, on average, mine do spend 75% of their time in the upper section of the tank. It is odd yours haven't learned to come to the top for food, at least. But I'm sure they will--turbulence and light won't stop a hungry fish!

Enjoy your fish, its fun watching them develop.

Don't worry too, too much, just make lots of water changes while the cycle is going on. All your Cardinals may survive if they were healthy when you got them. If you are really worried about them do a 50% water change every day. They certainly aren't in any danger now, except for moving stress, given your levels are good.

Make sure they have a nice low stress environment with places to hide, such as fake or real plants.

Looking it up, it seems Cardinals might like it 77 degrees, but check the web for multiple sources, I only looked at one.

But above all--Don't Panic.

Don't shy away from cardinals and neons, they're a bit more delicate than white clouds, but not too much so. They're beautiful, fun little fish to have. My neons amuse me every day with their games of tag, and when friends see my tank they always like 'the little blue and red fishies' best.
If you do 50% water changes daily, using dechlorinated water of the same temperature as the tank, the ammonia and nitrite levels should stay under control as your cycle progresses. If you're seeing nitrite, you're halfway through, so just keep on with the good work and you'll soon have a fully cycled tank.
As for when you should expect to see your cardinals die, hopefully they won't die at all if you keep on top of those levels. Use their behaviour as a guide - if they look ill, get in there and do another water change. Frequent (even twice daily) water changes won't slow your cycle, just be sure to only rinse the filter media in tank water, never under the tap. The filter is where the bacteria you're cultivating grow, there's virtually none in the water itself.
One note, as for the Cycle, many people don't think it does a thing. IME, it's never made a difference in how fast a tank cycles - might as well add it if you've got it, but many people will tell you it's not really worth the money it costs.

I believe RTR determined/discovered that while Cycle does not contain the bacteria which will survive in an aquarium, it does contain nitrifiers that consume ammonia--they just can't setup shop. So, if you keep adding it to the tank, it will reduce a bit of the ammonia, but not enough to stabilize the system. Doing water changes to prevent the ammonia from exceeding 1 ppm will be better for the fish and the tank in the long run.

Doing water changes will always help.

Fish change color according to light, stress, temperature, etc. If you look at your fish without the lights on, most will be pale. Flip on the lights, and they sparkle. Stress can cause changes in color and behavior--but it's important to realize that this change lasts for at least one day--2 or more in most cases. Depending on temp, you may have problems. Clouds can toleratehigher temperatures, but the cardinals will be prone to ailments at lower temps. They won't be ideal tank mates, but you'd be better off going with the lower temperature in the cardinals range.