Let's start with some definitions.
Object Projection:
At-Will Psionic, Teleportation
Minor Action Personal
Effect: You teleport an object you are holding in one hand to an unoccupied square within 10 squares of you or to a willing creature within 10 squares of you.
Object Projection is part of the "wild talent" power group.
I'm going to presume that it is accessed by taking the feat Wild Talent Master, just because it gives us so many more opportunities, especially when combined with Psionic Image.
The most obvious combination of the two is to steal and replace an item. We perform a stealth check to remain unobserved such that we can get into position, then we pick up the item, teleport it somewhere useful, and replace it with its image. The teleportation aspect is useful, but not essential here (though if you can pull this off, as a DM, I would be willing to house-rule that having either of these powers gives you a significant bonus to the thievery check. Beyond that, if your GM is willing, nothing is more disconcerting than stealing the MacGuffin of princess-slaying before the ritual starts, but not having anyone notice.)
The utility of this capability, of course, is a function of your game. It'll be not particularly useful in a dungeon crawl; and it's not useful --save as a source of narrative validation-- as a way of making money.
On the other hand, you can certainly cause a headache for your DM by combining it with Nimble Fingers, which explicitly allows you to steal sheathed items. The important thing here is that teleporting the target's weapon 10 squares away, perhaps into the fighter's hands (ready to stow in her pack), presents a signficant challenge to the villain retrieving it. This setup is, of course, excruciatingly difficult to pull off unless your DM provides for it; it would be quite reasonable to use this to deny an enemy attacks with the "weapon" keyword until they could contrive to find a bloody weapon, made all the harder by the fact that they can't somehow grab it out of your hands.
Another useful role is in getting stuff out of constrained spaces. If you're using Break & Enter or other third-party stealth rules, performing burglaries will be something done as a matter of course. With Object Projection, the fact that you are on a third story catwalk will matter naught for hauling the loot out of the location. As you can teleport your purloined goods to your confederates outside by looking out of a hole drilled into a window. (You did bring your hand drill, right? Good.)
Similar object passing is of course possible in dungeons, given the need to pass an object through a confined space. While this is not normally a problem, so long as your DM is collaborating with you about the environment of the game, there may be plenty of fascinating ideas for you to pass your party a key from the other side of a lock.
Your case 2 assumes that your targets are not capable of trivial correlation.
In a general sense, this should provide a situational bonus to some thievery checks assuming that you can enhance the narrative with its use, and make other thievery checks possible that would not otherwise be the case. You'd likely be more interested in the gauntlets of remote action or the Prison of Salzacas as more generally useful solutions to the problem of spooky action at a distance.
I recommend negotiating classes of capability with your DM while getting your character approved. Almost all interesting uses here are the pure domain of role-playing, and getting advance sign-off will reduce unhelpful arguments at the table.
