showposts, numberposts, posts_per_page, $qstring, $args… confusion

The full title of this question, which wouldn’t fit in the title field, should be:

showposts, numberposts, posts_per_page, $qstring, $args, get_posts, query_posts, WP_Query constructor confusion

I would like to ask WordPress gurus to answer this simple question:

Which of the following:

• showposts,
• numberposts,
• posts_per_page

is supposed to work with:

• get_posts(),
• query_posts(),
• new WP_Query()

when passed using:

• “foo=bar”
• array(“foo”=>”bar”)

These are actually 18 yes/no questions. Please answer all of them. I will print them in a tabular form and tack to my cubicle wall.