The cabinet is inside the vivarium.
Ornaments are placed from the Shop tab while you are looking at your tank, so you can see how they sit against the leaf litter and the branch.
River stones, a pale shell, a marimo ball, and a driftwood branch are free. The brass lantern, stone pagoda, mossy skull, ceramic hide, mushroom cluster, cork bark tube, stone ruin, and glass mushroom unlock one at a time. Each one can be bought with dew or with a small one-off purchase.
None of the ornaments change growth, breeding, or the rarity of an egg. They are there to make the tank feel like a place you chose.