This is my 2 cents worth and Congrats on your little fry
When I have my fry, I use 50% water from the parent tank and 50% clean water at first. I never really worried about cycled water with fry. I would keep the air stone going for movement and oxygen exchange.
As for feeding I use flake food that has been crushed into powder form and some times I would hatch out brine shrimp.
I never used a filter until they were big enough to stay away from the suction. I have 20 day old cory fry and tried them with a filter yesterday, one got sucked in, so I stopped with the normal filter.
My set up since the day they hatched is they are in a 20 gallon, with an air stone and Aqua clear filter set to low suction and I covered the intake intake stem with a AquaClear Foam sponge that I cut a hole into to place the foam sponge over the intake steam.
The foam sponge gets dirty quickly so I rinse it out a couple of times a week.