Learn English – the difference between “as much as” and “much as”

Which and what have different meanings. Which is used in questions to ask somebody to be exact about one or more people or things from a limited number.

For example, you ask What name do you prefer for your son? because there are many possible names to give to a baby.
Suppose that you're instead talking to somebody who tells you that his wife prefers Michael, her mother prefers Andrew, and his mother likes Alberto. If you ask him Which name do you prefer? you are asking him the name he prefers from among those three; if you ask him What name do you prefer? you are asking him the name he prefers, including any other name that isn't Michael, Andrew, or Alberto.

In your case, Which is correct? could be asked to a person who is talking about two or more options, for example You could do this or that. Your question is essentially asking Between this and that, what is correct?

In many contexts, the meanings are pretty much the same, but you might hear finished more often than completed in casual conversation. For example:

I've finished my shopping.
She finished the song.
He finished the race.

I could use completed in those sentences – the meaning wouldn't change, but the register might sound off.

The word completed can convey some sense of accomplishment. In the context of a race, it might work when the race is a major achievement:

He completed his first marathon last year.

Homework, though, is not really a major achievement, so I think you'd hear finished more often in casual conversation:

“Joey, where are you going? Did you finish your homework?”

That said, you might see completed in more formal contexts, such as a paper on education, or a course syllabus:

Students must complete six homework assignments during the semester.