fish’s tail, which amongst us is considered so beautiful, is thought on earth to be quite ugly
This shows how humans compare other living things to themselves. Also, this could allude to the fact they think of them as soulless animals like dogs and cats in the catholic and christian ideals.
And then he kissed her rosy mouth, played with her long waving hair, and laid his head on her heart, while she dreamed of human happiness and an immortal soul.
The prince is clearly taking advantage of the mute little mermaid by "kissing her rosy mouth" and laying his head on her chest. The mermaid doesn't acknowledge this but is thinking about the immortal soul at the end. This shows even if love is in her heart, she is more invested in the immortal soul.
She has given us a knife: here it is, see it is very sharp
The knife given by the mermaid sisters could be a visual representation of "cutting out sin for god". You must get rid of the evil to be good. And judging where the little mermaid ended up, that could be plausible.
she gave up tending her flowers, and they grew in wild confusion over the paths
Tending to her garden could be a allusion to the little mermaids purity and how it is being tainted by the prince. Grew in wild confusion is the state of the little mermaids mind being taken over by "lust" or the idea of gaining a soul.
twelve oysters on her tail
The twelve oysters shells on her tail give the visual representation of her rank in mermaid society. It could also be related to how beautiful someone is by the fact she put six on the youngest daughter and said "pride must suffer pain"