Распутать ветви, как распутать волосы, расплести косы у девушки. Зачем? Хороший вопрос. Наверное, что-то было связано с традициями плетения и расплетания деревьев.

"Разовьем мы кудряву": 1) "кудряву" means "кудрявая" (=curly as about hair). "кудрявая береза" is quite a common expression in the Russian poetry, traditional fairy-tales, etc 2) When a woman wants to make her hair curly, she "завивает волосы". 3) "развить" in this context means "uncurl" — "we'll uncurl the curly birch".

It's a very figurative expression. Something to do with romance and or joy or with whatever else. All references to trees and actions revolving around the trees, in very old folk songs, mean usually completely different things, nothing to do with trees.