I'll make some comments which will partly repeat what has been suggested, and likely add.
First, you will not likely get any fry if you leave the fish to spawn in a tank with other fish. All fish will devour any egg they find, and given the cory method of spawning the aquarist is very unlikely to be sitting there when each egg is placed in order to rescue it. Move the three cories to the 10g, on their own. I posted some photos this morning in your older thread of my pygmies in a 10g, there were more than 20 fry survived over several months and that was with no interference from me.
Second, put dried leaves in the tank. These decompose and produce copious amounts of infusoria which is the first food of any fry. I added no other "fry" food, just shrimp pellets for the adults, and the fry grazed the leaves and quickly learned about the shrimp pellets. Note, dried leaves, never fresh. Leaves that have fallen from the tree (as in autumn) and then completely dried. If the collection site is safe from pesticides, chemicals, etc, just rinse the leaf under the tap and when dry bag them and add a few to the tank. Most hard wood is safe, oak is ideal, also maple, beech; Indian Almond leaves can be bought in some fish stores.
Chunks of bogwood and plants will encourage "critters" and that is more good food. Any plants that will grow in your tank are fine. Floating plants are good because they are "ammonia sinks" but they also shade the light which tends to calm most fish. Alder cones add tannins and may help lower the pH (not suggesting this is necessary, just it might occur, depending upon the GH/KH/pH of the source water).
You must have a substrate of sand. No fish should be in a bare-bottom tank, it is stressful because it is unnatural, they can see reflections and they cannot filter feed. It is also biologically risky; the substrate sand is the primary and most important filter/bacteria bed in a fish tank.
I've no idea of the flow from the filter, but I suspect it is more than you really want; I use a single sponge filter (connected to air pump) in my smaller tanks, everything up to the 40g, just to provide gentle water movement. This description of the natural habitats of this species is instructive as to its need for quiet waters:
Has mostly been collected from marginal channels, backwaters, swamps, floodplain lakes, and smaller tributaries containing shallow, clear-to-turbid water with substrates of mud and clay. Some habitats contain no vegetation while others feature dense growths of submerged grasses, aquatic or floating plants such as Eichhornia or Pistia.
Temperature in the range of 20-25C/68-77F.
No cory eats plant/vegetable/algae so do not feed veggie foods. Insects and insect larvae form the primary natural diet, along with small crustaceans and worms,
C. hastatus is slightly different in that it is partially adapted to forage on pelagic zooplankton, meaning a diet containing plenty of live or frozen
Daphnia,
Artemia, and suchlike is recommended. The mini size of Bug Bites (they will sink and settle on leaves, wood, substrate) is ideal, along with shrimp pellets (I recommend Omega One), frozen daphnia (thawed first, it will sink too).