Part 1: Bee bait will only pipe into the "container" slot of the crucible furnace, with any method of item transport. Bait can still be manually placed into the input slots, however.

Part 2: Bee bait, fish bait, and I assume the other types of bait that smelt into fish food that are inserted into the "container" slot get consumed to produce fish food without needing heat/fuel. I assume this is because the furnace is treating them as a single-use fluid container?