Answer:
It is not a lyric poem it is narritive but the second answer is right.
Rainsford's first night of the hunt was spent in a big tree. "big tree with a thick trunk and outspread branches. He climbed up into the crotch and, stretching out on one of the broad limbs, after a fashion, rested.
If the underlined phrase is <em>born in New York in 1856, </em>then that would be a participial phrase, which often functions as an adjective in a sentence, like is the case here.
Gerund is always used as a noun, and infinitive has the form <em>to + verb </em>(to go, to be...)