I find that hi hats tend to be too loud actually. I usually end up muting the hi hat channel in mixes as the overheads pick up plenty. Sometimes the hats can even overbalance from within the overheads, that's why I usually play lighter hats and sometimes I find myself using two tops (lighter cymbals are generally quieter).
That would vary with every song and every section of that song.
Impossible question, everyone's sitch is different.
Like MikeM said, you have to mix yourself, according to what's needed. Sometimes the hats are prominent. Sometimes they are way under everything. Whatever it takes, or not.
On the same song, I'll bring them down for the vocals, and sometimes bring them up for the solo parts. As a general rule, I don't need to "cut through" but some music needs that from the drums. It all depends.