Shall is pretty much an archaic construction today, with the few minor exceptions mentioned above like „shall we leave now“ which can always be substituted with „should we leave now.“ Shall could easily just be dropped from the language, and probably should be, with „will“ or „should“ being substituted in its place, and no one even miss it or notice it being gone. Any distinctions anyone tries to draw between „shall“ and „will“ today are artificial. We know today a „rule“ was invented by some bishop in the 17th Century about this, who tried to say „shall“ should be used in one way and „will“ in a different way but, noted linguist and intellectual Noam Chomsky calls this distinction complete nonsense.
In a lot of older texts, you can read it as being equivalent to "will". In most forms of modern English, it's used for suggestions that are formed as questions - for example, I would never say "I shall go to the shops" (instead, I would say "I will go the shops"), however, you could say "Shall we go to the shops?"
I hope that helps! :)
Thank you, SHL.
Lucky me, this is my second attempt as I posted a similar question some time ago, I have the whole picture now:)