***** NOT A TEACHER *****
Hello, Zoltankr:
You have already received the answers to your questions.
I just wanted to share some information that may interest you.
*****
1. In English, sometimes there is more than one way to analyze a sentence.
2. "The girl came running."
a. One analysis claims that in older English, there was the preposition "a": The girl came a-running. And, as you know, an -ing word after a preposition is defined as a gerund.
i. Therefore, one can say that in "The girl came running," there is an "understood" preposition; thus, "running" is a gerund.
b. Another analysis says that in "The girl came running," the -ing word "running" is a participle.
As you know, a participle is used as an adjective.
i. Therefore, this analysis claims that "running" modifies (refers to) the subject "the girl."
*****
3. "Let's go fishing." According to one of my favorite books, you have this choice of analysis:
a. "Let's go fishing" = "Let's go a-fishing." ("Fishing" is a gerund, after the preposition "a.")
b. "Let's go fishing" = "Fishing" is a participle that modifies (refers to) "us." ["Let's" = Let us.]
I do NOT know which analysis is preferred by most American teachers in 2014.
James
Sources: Pence and Emery, A Grammar of Present-Day English (1963); House and Harman, Descriptive English Grammar (1950).