This question is a follow up of my previous question.
Q1: By having a list of homotopy groups and given dimension $n$, Is it possible to recover the topology?
According to WikiPedia: Topological spaces that are not homeomorphic can have the same homotopy groups.
Q2: Can anyone give an example of the above fact for smooth manifolds such that they have same dimension?
Q3: Can the homotopy groups determine the Euler characteristic?