It’s going to take 3 days to get up to 20 eggs, so should I just store the eggs on the counter until I have enough?
Ideal storage conditions for hatching eggs is around 55 degrees Fahrenheit, about 80% humidity, either laying flat or pointy side down, and turning them a few times a day. Avoid areas where the temperature cycles from warm to cool and back, stay out of sunlight hitting them, and stay away from AC or heating vents blowing on them. If stored this way they can last two weeks or more before starting them.
The closer you can come to those conditions the longer they will last. Very very few of us have these conditions but we do the best we can. I keep my eggs in a drawer in a dresser in a spare bedroom to keep them away from the dog. They are room temperature (in the 70's Fahrenheit) and humidity is usually fairly low from heating or AC. I store them flat and turn them 3 times a day. I number mine from 1 to wherever it goes (20 in your case) and put a red number on one side and a black number on the other so I can tell when they have been turned enough. I turn them by rolling them over. There are other techniques if you store them pointy side down. They easily last a week stored this way but two weeks is a bit too much for optimal hatching.
Since the eggs will hatch on different days, what do I do with the chicks?
The 21 day thing before hatching is an approximation. It is very possible some could hatch as much as two days early or late and you still get healthy chicks. There are different reasons the hatch can be that different: heredity, humidity, how and how long the eggs are stored, and just basic differences in eggs. A common reason the entire hatch may be early or late is the average incubation temperature. If it is a bit warm they can be early, cool and they can be late. A lot of my hatches under a broody hen or in my incubator are over within 16 hours of the first one hatching but I have had some go well into the third day, well over 48 hours.
As Junior67 explains above, the countdown to hatch starts when incubation starts, not when the egg was laid.
How long do I leave the chicks in the incubator before moving them into a brooder?
A healthy chick absorbs the yolk before hatch. They can live at least 72 hours without food or water because they live off of that yolk. That's nature's way of allowing the hen to stay on the nest and hatch late chicks instead of having to immediately take the first to hatch off of the nest to get food and water. I had one broody hen that hatched at least one chick late on a Monday. She did not bring her chicks off of the nest until Friday morning, about 80 hours later. All of her chicks were fine.
I leave my chicks in the incubator until the hatch is over.
