There is no difference in meaning between these three sentences, unless the speaker already establishes a context.
He's a bit angry
This means he is somewhat angry.
He's a little bit angry
This means he is somewhat angry. No native speakers would infer any qualitative difference in how angry he is, unless someone first said
John: He's a bit angry (meaning fairly angry)
Mary: No, he's only a little bit angry (meaning not as angry as John implied)
When used alone, "little", "bit", and "little bit" all mean "small". But if you emphasize "little bit" over "little" or "bit" then you are emphasizing how small it is.
If I walked up to you on Monday and said "I'm a bit hungry", and on Tuesday I walked up to you and said "I'm a little bit hungry", there is no way decide that I'm not as hungry Tuesday as I was Monday. But if on Wednesday I said "I'm a bit hungry", and you said "Have a hamburger", I could clarify that I'm not as hungry as you think, by saying "I'm only a little bit hungry".
Sitting at the end of the stairs, sobbing, having lost my love, career and self-respect, I say to myself, "Who AM I? What is the purpose of my life?"
See, here it is a question. That's why the helping verb (am) is coming before the subject (I).
I ask myself who I am.
Here, it is not a question, a mere narration of what I ask myself. So, it is not ending in question mark, plus, helping verb is after the subject.
Best Answer
The first implies that you are offering help to someone and want to know if he would allow you to do so. The second implies that the person is looking for something/help and you want to know if you can do something for him. It could be used in situations where you go to your boss's office for something and he may simply say if he can do something for you. They could be used for the same thing in certain situations but they don't mean the same thing.