Ex.: Marcio asked Dale´s a research on Rocket Science.

"Dale's a research"?  Is this just a typo?

Márcio asked Dale to do some research on/about rocket science. = ok

.... 

     Ask about - perguntar sobre...

     Marcio asked about the last Valeska´s  research.

Sorry, but this makes no sense.

Marcio asked about Valeska´s last  research. = ok

Marcio asked about the last research that Valeska did. = ok

.... 

     Sometimes, I have seen "ask for" with a certain "negative" bias, wether it is in a open or subtle way:

      a-) I have a lot of troubles, for example, this headache!

      b-) Serves you right, you drank like a fish yesterday.

I am sorry, but I don't understand.   "To ask for" is "pedir".  There is nothing negative I know of about the "for".  It's there.  It's used.  Sometimes it's dropped although it would still be translated as "pedir", but I see nothing "negative" about this practice.  Perhaps "pedir" and "perguntar" are being confused.