With cories, with breeding its more ideal to have 1 female to 2 males, but they will breed just fine with 1:1 too. They don't stress each other out like livebearers would.
For cory breeding...
I'll address the hybrid question. Yes some can interbreed, and it is generally frowned upon in the hobby.
Best way to prevent this is to have large enough groups of both species with different genders for both so they have their own mates to choose. They will choose their own over others if they have the option.
Certain lineages of cories are more compatible for interbreeding, if you check planet catfish you will notice a code with their name, this stands for which lineage of corydoras that species is. Any in the same lineages are able to crossbreed.
Now things that trigger corydoras breeding.
1) being well fed. Many people intentionally breeding cories will condition the breeding group with live foods twice a day.
2) cooler water changes. Frequent, large water changes using colder water often triggers them as this mimics a rainy season.
3) faster current. Again, mimics the rainy season which they breed in.
4) in some cases, softer more acidic water can also be a factor.
5) storms and weather fronts in the area will sometimes trigger spawning in cories. Those intentionally trying to spawn them will often time their water changes with weather systems.
6) winter often triggers some to spawn because naturally in the wild, this is their breeding season.
Many will eat their own eggs or other fish in the tank will. So if cory fry isn't something you want, don't remove the eggs.
If you want fry, collect the eggs by gently rolling them off the glass with your fingers and place them in a container with shallow water taken from the parent tank, use an air stone. Add a few drops of meth blue or a couple alder cones to prevent fungus. After 3-5 days the fry hatch. For first 3 days they feed off their yolk sac, but once that's absorbed they need to be fed several times a day on a fry starter food, infusoria, live baby brine shrimp, live microworms, or live vinegar eels until they grow large enough to eat crushed pellets/flakes. Water must be changed daily on fry tanks to encourage full growth.
