Oatmeal is the easiest breakfast. Before our trip, I pre-measured 1/2 cup rolled oats in snack size Ziplocks and added raisins, pecans, and chia seeds to the bags. When we wanted oatmeal, I just added 1 cup water and microwaved it in a bowl. We did bring a couple of 2.5cup Ziplock/Gladware plastic containers for this purpose as I wasn't sure how paper bowls would hold up. We don't like sugary oatmeal so that's why I did it the way we did -- but you could buy instant oatmeal packets if you want.
You can also order dry cereal and just buy a quart of milk at the CSR gift shop (Panchito's is what it used to be called, not sure if it still is) if your family likes to eat cereal for breakfast. We only eat cereal as a fun snack because it doesn't have enough protein to fill us up!
Or, you could go a different route and either buy yogurt at the resort (which is pretty pricy) or place a Garden Grocer/We Go Shop order and order perishables.
I don't see why you couldn't bring your own microwave. I do think CSR has some microwaves available to reserve but I'm not positive.