There are different fingerings for all scales; I felt these were the most common and easiest to play for me. What determines the mode you're playing is the root. For example, if a song was in the key of E minor, you would probably want to use the E Aeolian or E Dorian modes because they are minor and they are, of course, in E minor. The fingerings don't matter too much, it's what notes you use to create a certain type of sound.

Three notes per string is common because it's naturally easy for the fingers to play quickly. Usually I use my index, middle, and pinky fingers for three-note-per-string patterns.

To some degree, these patterns can fit in other places, but these fingerings go 2 octaves in the same position, so it's a little easier. The most important thing is what notes you are emphasizing that determine the mode. In E minor, plaing E Aeolian, you'll probably play a lot of E's since since it's the root.

There are no real rules for this kind of stuff, so it's a little vague. You just have to do your best to work through it.