When writing seventh chord inversions, how do you know if the notes should be placed to the right or left side of the other notes? Sometimes I see a 1st inversion seventh chord with the root placed to the left of the three notes below it, and sometimes to the right. This also seems random with second and third inversions.
It's fairly simple: if you are writing a block chord of any sort that contains the interval of a second, the lower note of the second is to the left, the upper note is to the right.
If there is more than one interval of a second, the lowest is to the left, and the notes alternate sides. The exception here is for even numbers of seconds (the intervals, not the notes) on downward-pointing stems (see the examples with asterisks).