I'm trying to understand some basics of stacks in algebraic geometry and have three questions:
1) As far as I understand, the moduli stack of vector bundles over a scheme $X$ is a replacement for the non-existent moduli space of vector bundles over $X$. Is this the only reason for the study of this stack or isn't it actually important to remember the isomorphisms between vector bundles?
2) What about replacing schemes by manifolds and define moduli stacks in a similar way? Does it make sense to talk about about stacks in the "euclidean" topology on the site of open subsets of euclidean spaces? Of course it makes sense, but I'm wondering if there is any literature about it. For example, is there a "generalized manifold" $BGL_n$ such that for every manifold $X$ we have an equivalence of categories between $Hom(X,BGL_n)$ and the category of vector bundles on $X$?
3) The objects of algebraic geometry have made a great evolution in the 20th century. Projective varieties, schemes, algebraic spaces, stacks. Is there an "upper bound" of this process of abstraction? I think that each abstraction was motivated by concrete geometric problems, but it might be argued if we actually solve these problems just by enlarging the category of geometric objects in consideration. This leads to the vague question: What are the fundamental ideas of algebraic geometry which will hopefully survive the next abstraction?