In The Dolphins, a dolphin which has been captured and trained for an aquarium show mourns its loss of freedom. In addition to critiquing humanities' treatment of wild animals, it also presents a wider critique of ecological destruction.
The question poems the lines out of sequence. We'll start with the earliest one from the first stanza.
"Outside this world you cannot breathe for long."
"This world" is their current world, the aquarium. The dolphin is longing for escape, but it has no means to do so. Even if it could escape the confines of the pool, the only place to go is dry land. Dolphins, as mammals, do breathe oxygen but their bodies are built in such a way that they require the buoyancy and support provided by water to extend their ribs and fill their lungs. Hence, travelling over dry land for an extended period in an attempt to escape will lead to death by suffocation.
As in much of the poem, the word choice here is very clever. To "breathe" is commonly used as a metaphor for freedom. So in saying it cannot breathe, the dolphin is both making a literal statement and bemoaning its lack of freedom.
"for the world will not deepen to dream in".
In the third stanza, the dolphin has realised that it cannot escape its captivity. Here "the world" means its world - the world of the aquarium. It understands that that world will not "deepen". This is an interesting word choice: at face value, it means the deeps of the ocean, where a dolphin is free to swim. But it could also be read as deep in an intellectual or philosophical sense, further humanising the dolphin's narration.
This theme continues with the conclusion of the line, "dream in". To dream is a very human activity: we do not really know if dolphins dream. But one can also day-dream, a common euphemism for stirring creativity and thoughtfulness. The line recalls the slightly trance-like state assumed when we take light exercise. In the tight confines of the aquarium, the dolphin is not free to swim and dream as it does so.
In summary: the dolphin is realising the aquarium will never get any bigger, and that as a result, it will never be free to swim at leisure. The line expresses this in deliberately human language.
"out of love reflects me for myself"
Is worth quoting in full:
"The other knows and out of love reflects me for myself."
Because it harks back to a line earlier in the poem:
"The other has my shape."
Which would seem to indicate that "the other" is another dolphin sharing the pool. That dolphin has a similar understanding of their awful mutual situation but it can do nothing. Instead, it offers sympathy: it "reflects" out of "love".
"me for myself" is interesting as it is a statement of individuality. Many animals lack a sense of self and, when faced with a mirror, react as if it is another animal of the same species. In saying "myself" the author is stating the dolphins have sufficient self-awareness both to act as individuals and to sympathise with one another, yet more humanising characteristics to generate sympathy for their plight.