as a binding agent
Yes, but they are not vegan.
It helps to bind the pastry ingredients together it also adds moisture and richness to to the mixture.
You don't, pastry can be made without sugar. Sugar is only added if a sweet pastry is required.
mainly flour, eggs, water occasionally milk
There is really no reason, it just is in a pastry because you need oil to make it
you shoot it with air and then boil it
Its raising agent is the high water content, which boils during cooking, puffing out the pastry. Unlike puff pastry, it uses eggs.
there is always a need for chefs of any kind
the eggs help bind together the dry ingredients and add color and flavour
No it doesn't.
the eggs are used in recipes because they have the nutation's to make the taste and to mix the flower and sugar.