Depending on the birds, some will get egg several times a day; breeding, feeding chicks, molting, recovering from being plucked, etc. These are times when they can benefit from the extra protein, so I give them more.
Others only get egg once a day or as I can get egg to them.
Greens, it depends, I can't pre-prep my greens (lettuce), so I have to chop it just before serving. Thus they get greens less often than I would like to. If I can do brocoli tops or something that I can prep and put into a plastic jar and put in the fridge, then it would be easier to feed them greens more often.
How much?
I give them as much as they will eat in a few hours. If you give too much, and they don't eat it in say 3 or 4 hours, it could spoil and make the birds sick. So I give only 1/2 teaspoon or so, depending on the bird and number of birds.
Now, as to the question, will they eat it? You just have to give it to them and see. Sometimes it will take them a while just to try it, other times they will just dive in and scarf it down. Depends on the bird and the food.
Example, I have NOT been able to get my female gouldian to eat eggs or greens. She will eat some of the stuff in Miracle Meal, but not fresh egg.
On some of my birds, I had to "train" them to eat the egg.
I removed their feed the night before, so when they wake up they are hungry. The only food I put in at "lights on" is a small bowl of egg. I would leave ONLY the egg out for a couple hours, then put their regular feed back in. It took a while, a few days up to almost 2 weeks before they would eat the egg on their own. If they are "stubborn" I lengthen the time before I put their regular feed in.
This is where I got the method from
http://www.finchinfo.com/diet/introducing_new_foods.php
Once they eat the egg on their own for a few days, I leave their regular feed in. Some are still hesitant, others will charge the egg when I put it in the cage.
Gud Luk.