It really doesn't matter as long as you have your Xbox 360 in a wide open space, free of dust and smoke, on a hard surface such as wood and not near any heat sources such as radiators and cookers. Ive had mine vertically on wood for a while now and ive had no problems what so ever, no scratched discs or overheating and no freezing or lag.
Hope this helped.
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Vertical, this reduces heat flow through your 360 system, keeping it cooler, reducing chances of red rings of death (RROD).
The xbox 360 can badly damage disks if you tilt the xbox from horizontal to vertical (or vice versa) making them to the point of unreadable
You can't choose between vertical and horizontal split screen unless it is an in-game option.
You can put it both ways, just not totally upside down vertical or upside down horizontal.
Yup