You can put a hexagon mold in front of a queen to make her spit out her jelly into the mold. When it comes to item transportation, the easiest ways are definitely long distance funnels and hovering hands.
You can use the gentle care robot in feeder mode to refill the furnace. There is no way to make structures work faster, except for a select few, like the furnace. You can measure its temperature using the inspector panel, and the hotter it gets the faster it cooks, but it also uses up the graphene faster. You can cool it using the cryo generator.