Hydrogen reactions with catalysts
Adding a bit of information for your question a). The reactin we are looking at is:

$$\ce{2 H2 + O2 -&gt; H2O}$$ 

As you can clearly see, the final product water has one oxygen atom for 2 hydrogen atoms, while in the beginning, we only had diatomic molecules. This means that during the reaction, at least one fo the diatomics had to break to single atoms. In this case, this happens with the reaction:

$$\ce{H2 -&gt; 2H^.}$$

From this step, we have a nice reaction scheme called a radical chain reaction. However, we first need to break the $\ce{H-H}$ bond somehow, and this is what flame is doing. If you break a significant amount, then you don't need to provide flame anymore, the reaction is self-supporting — the flame is ignited.

Now, a catalyst is doing exactly this. Many metals, including copper, can adsorb hydrogen molecules to the surface, and this also results in breaking the $\ce{H-H}$ bond — so the explosion can start this way too.