1. I would say always pattern the feature or body instead of the sketch. I don't like linear sketch patterns at all. In addition to just working better, a pattern of the feature or body will be much easier to edit.
2. If you're creating one hole first, and then patterning the feature, it's no problem to pattern in two directions in one operation.
3. I rarely use the circular sketch pattern, so I'm afraid I can't help with that one or comment on how well it works in general.
4. You didn't ask, but while I don't use linear patterns in sketches, I use the mirror function in sketches all the time and it generally works very well.
In order to select the 2nd axis for a rectangular array you first need to increase the # of instances from 1 to 2+, then it will let you pick that axis.
The answer to 4 is there is a point in the center that the pattern is picking up.
Thanks! Mysteries solved, and I'll start using feature vs sketch patterns.