According to this question and answer from Machon Shilo it seems that one is allowed to say at least one of the prayers in Hebrew.
However, some prayers may not be said in Hebrew, for example the kedusha d'sidra which if said in Hebrew could be confused with the Kedusha of the Shemona esrei.
Regarding the prayer of "Brich Shmei", the prayer itself comes from the Zohar, long after Aramaic stopped being the common language of the people. Since the prayer is from a late origin, that gives strength both to the argument that it should always be said in Aramaic, and also to the argument that since it is a personal prayer, one may even say it in the language they are accustomed to. It was a tradition in my shul, that a Bar Mitzvah would say this prayer in English to themselves before concluding the prayer in Aramaic for the shul as a whole. But this was only done on the day of the bar-mitzvah itself, and never during the rest of one's life.
Each prayer that is in Aramaic needs to be looked at in detail to see why it's said in Aramaic and what the ramifications would be if it was said in Hebrew.