1 I do what the singer wants. Some like to do it in chunks (e.g. verses and choruses). Others like to do the whole thing. Sometimes I will suggest that they do it in chunks if they are struggling with the whole thing.
2 I aim to get something good in the first two or three takes (and often the first is best). If it hasn't happened by then, there's little point in continuing. You can end up with either lifeless performances, or diminishing returns (one problem fixed, but a new one emerging).
3 I'm more interested in the energy of a performance rather than its technical accuracy.
4 I record with nothing in the signal path (no EQ, no reverb, no compression etc). Sometimes, though, I have fed reverb back to the vocalist if they insist. I don't like doing this because it can make them sing flat. Loud bass can affect their pitching as well.
5 DC offset and zero crossings: I don't worry about.
6 I don't sweat too much on 'mistakes'. In most cases, these exist only in the eye of the performer. The listener would not realise that it was a mistake. However, I don't mind dropping in on sections where something bad has happened, but there is little to be gained by redoing the whole thing.