Probably a bug in these snapshots that Mojang made.
Go to edit your profile and allocate more ram in the JVM args. For example, -Xmx(#here) -Xms(#here)
Anything that's wood including stairs, will burn if a fire entity/block is within 3 blocks of a flammable block. (Even wool)
This is caused by server-side or client-side lag. Should allocate more ram to fix.