The first stanza describes the tree as a "giant," powerful enough to resist the creeping vine wrapped around it like a python. The tree has scars but still lives and reaches up to the sky (stars). The tree is old but full of life; in itself and as represented by the birds and bees around it. In this sense, the tree symbolizes life but more particularly, the tree is a metaphor for memory. This becomes more clear in the subsequent stanzas.
In the second stanza, the speaker notes more signs of animal life (baboons and birds - kokilas) and the water-lilies. Although the tree is teeming with life, the speaker adds that it is the memory associated with the tree that makes it so important to her. In the third stanza:
Beneath it we have played; though many years roll,
O sweet companions, loved with love intense,
For your sakes shall the tree be ever dear.
The tree is literally the place where the speaker and her companions played, so it is an actual, physical place of memory in addition to being a metaphor that symbolizes memory. Just as a family tree shows how family members are connected, the speaker sees this tree similarly in that memories shared with others are connected. This goes for happy memories as well as the sad ones ("dirge-like murmur" suggests memories of loved ones lost). There is a suggested allusion to the Biblical "tree of life," and the garden of Eden. This gives the place/metaphor a sense of paradise; in memory, it is untouchable, even potentially eternal.
Note that it is "our" (not "my") casuarina tree. The tree is a symbol connecting many lives, many memories. In closing, the speaker hopes that when she is gone, there will be more "deathless trees" in addition to this particular tree. Here, again, this can be a literal tree (capable of symbolizing and providing an actual, physical space for memories) or the tree as metaphor for memory. Paralleling the tree metaphor of memory is the poem itself. The poem itself is the speaker's humble attempt to do what the tree has done for her: serve to remember her life and those who she called companions. The poet invokes Wordsworth's "Yew-trees" with the "Borrowdale" reference; this underscores the idea of a poem as a written memory.
Thank you for the quick response to my question. It's given me some points to base my answer on. I appreciate it.