On the Infinity Evolved 6 Building Competition server, my witch's cauldron vanished after harvesting it with a steel pickaxe. I also saw someone mention using flint and steel with a dispenser to heat a cauldron, but I'm not quite sure how to do that...
While I will leave someone else to address the first issue, I can quickly explain that you put the flint and steel into a Dispenser, aim it at Netherrack, and turn it on, usually via a lever. On some servers, like Regrowth, this is the only way to keep the Netherrack lit.