Stephen is definintly aware of his maturing. This is made obvious by his recollection of his time in school and he realizes that things that made him angry in the past (he being teased by Heron and others) no longer upset him. Stephen also is aware of his maturity near the end of the chapter as he feels distance from his father, repeating to himself the lines of Shelley's "To The Moon." And finally, at the end of the chapter as Stephen goes out looking for a prostitute, he is definintly aware how he and his body have changed.
I think that Stephen has stopped trusting authority in the second chapter, and really doesn't look up to those he would have in the past. Look at Mike Flynn for example. Even though his father has told him that Mike Flynn is the best coach, Stephen is suspicious of him.