Eggshells can be simply crushed by hand and placed in a bag in your filter or ground into a powder in something like a mortar and pestle to make it dissolve into the water a bit faster.
Banana plants can be propagated by waiting for the plant to send a leaf to the surface and then cutting that leaf and stem from the rest of the plant. Leave the cutting floating in your aquarium and it should start producing roots and new leaves near where the stem was cut. Once this happens, the roots can be planted in the substrate.
My algae is the only plant that pearls.