The sound of "I have eaten a chicken" sounds odd. I don't think I hear people say that too often. Usually people will just say "I eat the whole chicken". Your friend is correct. Often, the context dictates how the sentence should be constructed. That's the reason I thought the sentence sounds a little odd by it self.  

" I have never been there" means you have never visited this place in your life up to the minute you make that statement.

I've never been to New York in my life".

I've never been back to my country since I came to the U.S.

The difficult part for ESL learners in using the correct tense is recognizing when something happened and when something fisinished. In other words, finding the proper time window to build your sentence with. Here are a couple of contexts for your reference:

If my friend asked me to go dinner, I would say " Thanks for inviting me but I just ate" -- this is perfectly fine. You don't really have to say "I've just eaten", although it's also correct.

If my friend said "You look terrible; are you feeling ok?", I prabaly will say " I haven't been feeling too well with this flu for a few days". ---The present progressive paints a picture that you started  feeling sick sometime in the past and still feeling sick as you speak.

Hope this explanation helps.