POR: preposition that indicates 1) Cause, reason; 2) environment; 3) The place that something or someone crosses. PARA: preposition that indicates 1) direction; 2) purpose. Sometimes you can use both, sometimes you can't. In your examples you can use: "Can you do something for me?" = "Pode fazer uma coisa PARA mim?" or "Pode fazer uma coisa POR mim?; "This is a present for my mother." = "Isto è um presente PARA minha mãe."

"Pode fazer uma coisa POR/PARA mim?" < you can use both "Isto é um presente PARA minha mãe" < the present is for someone, use PARA"

It's kinda hard to define rules for the uses of these two prepositions, Clayton, just as it would be in english, if you think about the idioms. We have the same difficulty with the prepositions "for" and "to". And it kinda saves relation within a syntagm level. I'm gonna try to begin looking at the examples you gave and then try to go on a deeper level. Can you do something for me? - Você pode fazer alguma coisa para/por mim? - In this case the translation would be possible for both with a slight semantic difference. The "por mim" syntagm could emphasize better the sittuation of doing something in my place, replace me in doing something. Is that clear? I guess we could also see that the syntagm [para/por mim] relates to the verb "fazer" and not to the object [alguma coisa] This is a present for my mother. - 1. Este (ou isto) é um presente para minha mãe. 2. * Este é um presente por minha mãe. In this case it would sound strange for native speakers the use of the "por" preposition. I find it somehow acceptable, but they have different meaning. When someone says 2, it would mean you're giving a present in the name of your mother (in her place). I also guess it could mean you're sending someone a present through your mother (but it would be harder to express it this way). In general you could use those normative grammar conventions: "para - movement (tending to a limit, purpose, direction, perspective) por - movement (going through an extension between limits, duration) situation (result of the movement of approaching a limit)" (Cunha&Cintra - Nova Gramática do Português Contemporâneo)