1. Once I collect the eggs, should I wash them, or do they need to be washed before going into the incubator?
The standard recommendation is to only set clean eggs and do not wash them. Removing the bloom can make it easier for bacteria to get inside. But you are purposely setting dirty eggs you don't want to sell. A light bit of poop or dirt isn't bad but a clump of poop or mud can remove the bloom and house bacteria.
Hatcheries wash their eggs but I'm not a hatchery. I don't have a fumigation schedule for the room the incubator is in. I don't have the sanitation requirements for washing up and have sanitized clothing for anyone entering that room. But since your eggs are dirty, washing them and keeping everything as sanitary as you can is the best you can do.
Since you have an enhanced risk of bacteria getting inside I'd suggest every two or three days you sniff the eggs. If you smell a rotten egg smell get rid of that egg and wash your hands before you touch anything else. To me this is about minimizing risk not courting it.
2 How long can I store these eggs before they need to be incubated?
3. How should I store these eggs while I’m waiting.
These go together. The ideal temperature to store eggs for hatch is 55 degrees Fahrenheit. The ideal humidity is high, think in the 80% humidity range. You want the temperature to stay fairly constant, fluctuations up and down are not good. Try to avoid breezes from AC or heating vents from hitting them. It helps to turn them some, at least three times a day.
The closer you are to these conditions the longer they stay hatchable. It is not like they all stay great for a specific time then all of a sudden every egg goes bad. Some eggs can handle the wait better than others.
If you can meet these conditions they can probably last two weeks or more in storage. Very few of us have an ideal place to store them so just do the best you can. I store mine in a spare bedroom inside a dresser drawer to keep them away from my dog and turn them three times a day. The temperature is in the 70's F and humidity can be pretty low because of the heat or AC. I can store mine for a week and still get good hatch rates.
4. If a breed is sex linked, (barred rock Benz welsummer roo) how soon should I be able to notice the color markings? I’d assume after a day or two when the hens fluff up and fill in with down?
You should be able to see the spot as soon as the chick dries off. You can't wait very long and that still work, just a few days for the spot. Once they start feathering out you can see the barring on his feathers, probably wing feathers first. Her feathers will be solid black, no barring. The first post in this very long thread has photos of black sex link chicks. It might help.
Sex- linked Information | BackYard Chickens - Learn How to Raise Chickens
If you have other black chicks you will not know that any without the spot are actually pullets. You have to know which hen and rooster they came from.