You asked two questions so I have had to cut it down to one. In this poem the speaker contemplates a row of birches bent to the ground and he imagines how the trees may have changed their shape in this way. When nature itself bends the birches, during ice storms, they may stay bowed permanently. But the speaker prefers to think of the trees as bent under the weight of a young boy repeatedly climbing and swinging on them. The speaker describes this process on both a literal and a symbolic level. As a boy the speaker also climbed birches, blissfully ascending toward heaven but also gladly descending back to earth. As an adult the speaker remembers this oscillation between heaven and earth and longs to be again a "swinger of birches."
This climbing up the birches and then swinging back down again obviously operates symbolically in the story. It seems that the theme has to do with the human desire to accomplish something extraordinary, represented by the climbing up to "heaven" on the birches, but at the same time the poem states the necessity of returning to "earth" or reality, where love, which is the greatest human joy, abides. Note how Frost describes his desire for both states:
May no fate willfully misunderstand me
And half grant what i wish and snatch me away
Not to return. Earth's the right place for love:
I don't know where it's likely to go better.
I'd like to go by climbing a birch tree,
And climb black branches up a snow-white trunk
Toward heaven, till the tree could bear no more,
But dipped its top and set me down again.
According to Frost, therefore, we as humans need both - we need to be climbing and reaching towards "heaven" or the achievement of great deeds, but at the same time we need to return to "earth" to experience love.