So, could it be said basically that methods() are 'local', while functions() are 'global'? And further, new memory is allocated for each Method when a new instance of an object is created, whereas only one copy of a function needs to occupy memory and they all use that?
No it couldn't be said. :)
Methods will have only one copy of the code, just like functions. Even if you make 1 million instances (objects) of a Type.
Basically, Functions cannot access Fields nor Methods in a Type, because they are not working with an Object. They can access other Functions, Const's and Global's of a Type though because none of those actually require an object to work.
Aaron