Hi Mumof5 and welcome! You are right, your eggs can be cooked any way, just be conscious if you are adding anything when cooking them. Eg. A poached egg will have 4-5g fat whereas a fried egg will have an extra couple of grams of fat from the oil you cooked them in. A little extra fat isn’t going to hurt, but if you consistently have an extra 10g of fat per day, it will add 90 calories to your overall intake and if you are NOT burning the same or more calories, you could potentially store fat.
You can leave out the mushrooms or substitute for the same weight of another above ground veg.
I hope this helps!