Why this Nondeterministic Finite accept this string? I am reading in my book that this NFA machine accept the string 10100. If we follow the execution, we will find our self in branch with the state final q0. 

The only answer for me is that when we are in state q0 after 1010 and 0 is coming we can't move any more so this branch will die even it is in the final state. Am I right?
When a transition doesn't exist for current (state, input) pair, the NFA halts and the computation path rejects the input string. Or if an empty string transition is defined, it can be used to go into a garbage state for undefined transitions and the computation path rejects the string. See What does an NFA do if there&#39;s no transition with the correct symbol? for really good information.

In addition, this source that says the string is not accepted: http://people.cs.nctu.edu.tw/~wgtzeng/courses/FL2013SpringUnder/2.%20Finite%20automata.pdf slide 15.