Hi,
The independence he is starting to show is good, but the hitting is a concern (I would not worry about the raspberry). The worst thing you can do is reinforce the behavior by yelling at him (gives the behavior attention). I would suggest using I statements (I don't like it when you hit because it makes me feel . . .). Then I would calmly send him to time out for a set period of time. If it is continuous, I would ignore it, then the next time he asks for something, you say no.
The thing that I wondering, is where did he pick up this behavior? Did he get it at school/daycare? What TV shows is he watching, etc. My son, who loves spongebob watched the spongebob movie (which was far more violent than the tv show) walked around for two weeks threatening to pull off our arms because that happened in the movie, so they do pick up a lot of what they watch.
What you also have to remember is that he is not being disprespectful on purpose, but trying to forge independence. (I had to have this talk with my husband as well.) You have to remember every behvior of a child that age is designed to get attention, negative or positive. He may feel like he is not getting enough attention specifically from your fiancee. If I had to fathom a guess, I would say the behavior happens most when your fiance gets home from work and is trying to decompress, and not real emotionally accessable. If this is the case, you may want to have a routine where after a set period of time, your fiancee sits down with him to read him a story or something that is one on one time with the two of them. That may help the behavior dramatically.
Good luck.
L.