You don't need egg in anything for raising or the likes, so simply omit the egg. You don't need a substitute for it, it is merely a binding agent
Milk, easy, use soya or almond milk, or even plain water, if you had to.
Butter: again easy, soya marg had been my most successful substitute for cakes and the likes. I use Pure (which is a make) soya marg.
As for pancakes, well I have never put marg or oil on in them just on the griddle. Milk, flour, sugar, sorted.