What did he hope to accomplish by asking people questions? What was his view on why to bother living at all?
In Xenophon's 'Conversations of Socrates', Socrates is presented as a character who wants to understand the meaning of things. For example, he finds the man with the largest library in Athens, and then queries him on ethical questions.
It is implied that this is because Socrates thinks having so many books and thus so much knowledge should make the man the wisest in the city. His cross examination of the man's answers lead them both to conclude that books in themselves do not grant wisdom. Which is apparently disappointing to Socrates.
According to Xenophon's account Socrates does argue that there is civic virtue in helping one's friends, family, and city, to achieve success. This is not unusual by the standards of the time, so it is not especially profound.
There may be a clue from his trial. Socrates is sentenced to death by hemlock, and chooses to drink the poison, even after the court changed their mind and withdrew their death sentence. It has been suggested elsewhere that this decision was motivated by the desire to die a righteous death (put to death by a corrupt court), though it is never something he personally is meant to have said.
Regardless, his notorious trial in itself is a meaningful event, and from Plato's account we have one of his most famous quotations:
I am wiser than this man, for neither of us appears to know anything great and good; but he fancies he knows something, although he knows nothing; whereas I, as I do not know anything, so I do not fancy I do. In this trifling particular, then, I appear to be wiser than he, because I do not fancy I know what I do not know.
Socrates was intensely curious about everything, but unfortunately for him he never was satisfied with any wisdom he found. As in his trial, his inquiries proved the absurdities and limitations in what others held as deeply profound or sacred notions.
It is therefore odd to ask why he should choose to live. When he died he had yet to find the wisdom he spent his life searching for, but perhaps with his trial and death sentence he had realised it in intellectual humility.