並ぶ and 並べる: waiting lines and display order
Compare people lining up with arranging objects, distinguishing line position, arrangement criteria, and displayed states.
Wait in line
切符を買うために、列に並びました。 says that someone joined a line to buy a ticket. With 並ぶ, read ならぶ, the person joining the line is the actor.
二列に並んでください。 asks people to form two lines. 二列に gives the arrangement, unlike 二列目, which means the second line.
Put objects in order
本を高さの順に並べました。 says that someone arranged books in order of height. 並べる, read ならべる, uses を for the objects and に for the ordering criterion.
食卓に皿を四枚並べてください。 asks someone to arrange four plates on the table. 食卓に marks the location, and 四枚 gives the number of plates.
An arranged state and comparison
棚には新しい商品が並んでいます。 says that new products are displayed on the shelves. It does not imply that the products moved into line by themselves.
二つの写真を並べて比べました。 means that someone placed two photos side by side and compared them. 並べる applies to arranging things for comparison as well as forming lines.
Does 二列に並んでください mean to join the second line?
Show the answer and why
No. It asks people to form two lines. The second line is 二列目.