they are same. אבל is more useful in everyday language. אך is used mostly in books.
Why is "hu" before "kharif" but not before "taim"? Can it be omitted and added as wished?
You simply don't need it before טעים. The word אבל (but) has some negation in itself, denotes exclusion of something and because of that it feels natural to fill this gap with הוא. The whole problem comes back to the fact that in Hebrew one does not find normal "to be" stuff.
It's an oged, but in this context it's not completely necessary, הפלפל טעים אבל חריף is also acceptable.