Learn English – better phrase than “I felt rewarded”

You are correct in thinking that the original use of "violate", when applied to a person, is "rape". The use of violate to describe feelings is much more recent https://books.google.com/ngrams/graph?content=feel+violated&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cfeel%20violated%3B%2Cc0

I agree that online dictionaries don't seem to cover the issue. There are two aspects which seem clear. The first is that feeling violated refers to emotional distress caused by the inappropriate acts of others towards the speaker (one does not feel violated by seeing pictures of starving children, for instance - unless, perhaps, one is forced to look at them). The other is that there is no fixed threshold of offense. That is, there is no easy way to locate the transition between offended and violated. What is common is that the offense intrudes on the victim's sense of self, privacy or safety, just as rape intrudes upon the physical self.

How are you? is the natural, standard question for someone when you want to know about them. Use this between friends, etc. Alternatively, you can use the more colloquial "How's it going?"

How do you feel today? is a question that is looking for a contrast between today and some other time.

So, how do you feel today?

Much better than yesterday, thanks!

You can also use the present progressive to express a longer time when the other person may not have been feeling great.

So, how are you feeling today?

I woke up today feeling amazing! I think I've finally beat this flu.