For telekinesis, the target is "See text". For the combat maneuver area:

Quote Originally Posted by SRD, Telekinesis
Alternatively, once per round, you can use telekinesis to perform a bull rush, disarm, grapple (including pin), or trip. Resolve these attempts as normal, except that they don’t provoke attacks of opportunity, you use your caster level in place of your base attack bonus (for disarm and grapple), you use your Intelligence modifier (if a wizard) or Charisma modifier (if a sorcerer) in place of your Strength or Dexterity modifier, and a failed attempt doesn’t allow a reactive attempt by the target (such as for disarm or trip).
For the other? Anytime we've entered the floor or the ceiling completely, we've left the arena, by that standard. I just carried it farther.

Against a creature with constant see invis? It likely won't be incorporeal. I'll have ethereal shifting, and such. I admit, my damage isn't what I'd like. I may change it some more.

The alternate would have been to treat it as a thrown ranged weapon, if we can't go out of the arena, and throw it 50 feet away. (range increment 10, 5 increments. That would put it untouchable, outside the arena. Either way, I intend to put your shield where it won't be gotten. Only chance I've got is to lower your AC, AND be invisible. I'm at freakin' 1 HP. That's like, feathers kill me territory.