What is a "milonga"?

A milonga is a place where people dance (the) tango. - I would personally say "the tango" and not just "tango."
At the milonga, couples dance in a simpler way, and not as acrobatic as professional dancers. - don't know that "acrobatic" is the right word here, since tango dancers do not perform acrobatics.

It consists of making some shorter steps and walking elegantly without raising the legs. - raising them how? - I would elaborate

All the couples dance in the same direction, which is counterclockwise. The man leads the woman.

At times it can be quite congested on the dance floor, obligating the man to swing in the same place - not sure what you mean here and why you are using the word "swing"

in order to avoid stepping on other couples' feet.

 
The man invites a lady to dance using a gesture called the "cabaceo."

If the lady accepts the invitation, they proceed to the dance floor. If, however, she doesn't want to dance, she looks away. - I think this is what you mean here.

They are going to show you the eight basic steps to dance tango. - not sure who "they" is so can't comment on this