Is the direction of edges in a Bayes Network irrelevant?
TL;DR: sometimes you can make an equivalent Bayesian network by reversing arrows, and sometimes you can't.

Simply reversing the direction of the arrows yields another directed graph, but that graph is not necessarily the graph of an equivalent Bayesian network, because the dependence relations represented by the reversed-arrow graph can be different from those represented by the original graph. If the reversed-arrow graph represents different dependence relations than the original, in some cases it's possible to create an equivalent Bayesian network by adding some more arrows to capture dependence relations which are missing in the reversed-arrow graph. But in some cases there is not an exactly equivalent Bayesian network. If you have to add some arrows in order to capture dependencies, you might end up with a graph which represents fewer independence relations and therefore fewer opportunities for simplifying the computations of posterior probabilities.

For example, a -&gt; b -&gt; c represents the same dependencies and independencies as a &lt;- b &lt;- c, and the same as a &lt;- b -&gt; c, but not the same as a -&gt; b &lt;- c. This last graph says that a and c are independent if b is not observed, but a &lt;- b -&gt; c says a and c are dependent in that case. We can add an edge directly from a to c to capture that, but then a and c being independent when b is observed is not represented. That means that there is at least one factorization which we cannot exploit when computing posterior probabilities.

All this stuff about dependence/independence, arrows and their reversals, etc., is covered in standard texts on Bayesian networks. I can dig out some references if you want. 

Bayesian networks don't express causality. Judea Pearl, who did a lot of work on Bayesian networks, has also worked on what he calls causal networks (essentially Bayesian networks annotated with causal relations).