How to use this Japanese sentence "行ってまいります"? Learned it from the class but have no idea how to use it within a certain context. The translation of this sentence from google is "See you"

What does char "が" function here? I saw a Japanese sentence "居間に 父と母が います" with translation as "I have father and mother in the living room". So what does char "が" mean here? Any function or purpose of this char to be appended in Nonu? Thanks in advance.

How to translate "よろしくおれがいします" in English?

What is the difference between word "impudent" and word "impertinent"? According the the definition, word "impudent": not showing due respect for another person; impertinent. Then the word "impertinent": not showing proper respect; rude. I can not tell how to differentiate the usage between those two words according to definition. Any comment is appreciated!