Just like any automaton, a PDA is nondeterministic if (and only if) the transition relation is not a function, that is there are configurations that have multiple possible succeeding configurations. If this is the case for reachable configurations, this means that a non-deterministic automaton has inputs for which there are multiple computations.
Here, the transition $(\varepsilon, Z0/Z0)$ to state three may be taken even though the word has not been completely read, that is in configurations of the form
$\qquad (\alpha 1 \beta, Z0)$
you can either take transition $(\beta_1, Z0/\beta_1Z0)$ or $(\varepsilon, Z0/Z0)$ -- the automaton is non-deterministic. Of course, taking the latter always leads to rejecting the input unless $\beta = \varepsilon$, Since there is no other nondeterminism, this implies that the automaton is unambiguous.
Converting an NPDA to a DPDA is not always possible; NPDA define a properly larger language class than DPDA. Given an NPDA, checking if an equivalent DPDA exists is undecidable. And even if there is one (and you know that) there is no algorithm to find it. That is to say, there is no general, algorithmic technique for that part of your question.