1) It Is very likely that fire will happen although it may be rare, however which parts of the Rig Component will causes it? Will power supply goes on fire? Will the GPU gets too hot and the wood starts to burn up?
Parts of the rig that might catch fire;
1. GPU - since this is the most stressed part, I think that faulty gpu fan might atleast cause the fire
2. Risers - as we all know, there are no legitimate manufacturers of these
3. PSU connectors - I've seen somewhere in the forum that a connector melted due to the electric load
4. Motherboard - choose the one with solid state capacitors
I think it is good putting some fire resistant materials under your rig.
Also if possible, to lower the temp, you may put additional electric fan or blower in front of your rig.
If there are any windows, you may open that to improve ventillation.