Learn Hardcore Spanish (Spain): Mi amigo se cayó por las escaleras.

Spanish often uses a pronominal form to talk about involuntary or accidental events involving people. Caerse is the common way to say “to fall (down)” when the subject is a person. So Mi amigo se cayó sounds natural and neutral, implying an unintentional fall. Using plain cayó with a person is possible but sounds unusual or more formal/literary.

Can I drop se and say Mi amigo cayó por las escaleras?

You can, but for everyday speech in Spain it sounds off or overly dramatic (it can evoke “he fell in battle” or “collapsed”). With people, Spaniards strongly prefer se cayó. Save cayó (without se) for set phrases like cayó enfermo (“he fell ill”) or for objects in some contexts.

Why use por in por las escaleras? Could I use en, de, or desde instead?

por las escaleras = “down/along the stairs” (path or route). This is the idiomatic choice here.
en las escaleras = “on the stairs” (location). It means the fall happened while on the stairs, but doesn’t necessarily imply tumbling down them.
de la(s) escalera(s) = “off the stairs.” With stairs it’s not the usual way to say “down the stairs,” but with a ladder it’s normal: se cayó de la escalera.
desde la(s) escaleras focuses on the starting point (“from the stairs”), not on the path down; it’s uncommon in this meaning.