If a string(w) is accepted by an NFA, then corresponding to w, can there be multiple paths each starting from the start state and ending at an accepting state?
Yes, there can be many paths from the starting state to the ending state. It is not too difficult to cook up many trivial examples of when this happens, for instance
Clearly accepts the string $ab$ but it can go through either $s1$ or $s2$.
However, in DFA's this will never happen because at each state there is only a single possible transition for each character, and those fixed transitions uniquely determine the path.