How can a child learn from swinging Birches? What does Frost, looking back on the experience, gain from it? (How does he understand it as and adult who was “once myself a swinger of birches)?

You have quite a few questions here for this short space. One important theme of "Birches" is how Frost uses his poetic imagination to transcend the limits of the real world. He rejects the true reason the birches have been bent over in favor of his own fanciful explanation. On some level, he is claiming that this act of the imagination embodies a larger "truth" and is a worthy task, one that must be made with great care and diligence. Children naturally embody this kind of imagination.