Yes and yes.
Student or Learner
Yes and yes.
Is it the same thing like: They are going fishing?
fishing is gerund too?
***** NOT A TEACHER *****
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.
Sources: Pence and Emery, A Grammar of Present-Day English (1963); House and Harman, Descriptive English Grammar (1950).