I always say "happy to help!" after helping someone not because I'm actually happy to help them, but because I wish I really was happy to help.
I am not sure I understand. Why do you say it if you don't really mean it?
Because I realized that just saying "Happy to help" is better than trying to be happy to help.
It's good to help others, and I am glad that you are doing it.  However, it is still somewhat wrong to be lying about your intentions.  Perhaps you could just say "You're welcome" when they thank you, instead of implying that you actually feel differently.
I guess. It doesn't really matter since I will be saying it anyways.
It is good to help others at the end of the day. If you are being a good person that is what counts most.