During a use of TK to attack with an object,If A is an object, and b is an opposing character, if aB has shape change, do you get the SC roll? Or not because you are targeting the square not the character.

Well that depends, does the square have Shape Change as well? Can the square become a mop head or small area of marble in order to throw off its opponent? And if it can in fact do this, do you think the smartest thing to do is to attack the floor? Why not instead try to sell said floor for cash?

You draw Line of Fire to the square, but you still target the character, so everything that normally happens when targeting a character (except Line of Fire) still happens normally.

In other words, Shape Change can still avoid TK.

Just to confirm my statement, here is the text for TK, with the relevant portions highlighted:

Give this character a power action and designate a target character or object (A) and a destination square (B). This character, A, and B must all be within 8 squares and line of fire of each other. Place A in B. ... If A is an object and B is occupied by an opposing character, this character may make a ranged combat attack targeting the character occupying B, dealing object damage and destroying the object.

Note that Line of Fire only needs to reach B, the square, not the character occupying the square. However, the character IS TARGETED. Shape Change only requires targeting, so will work against TK.

1) yes, the square has shape change.
2) yes, it can become a mop head or small area of marble in order to throw off its opponent.
3) attacking the floor does have its advantages.
4) I think selling cash is illegal, maybe the floor and I could barter for the cash.

Since the attack and the targeting doesn't happen until after the object is placed, that means that a successful Shape Change roll means that the object is just left sitting underneath the intended target, right? It makes TK attacks a tiny bit riskier, since you can't pick a new target like you normally would for Shape Change.

Yes, because you're choosing a square for B, if Shape Change is rolled, you will be limited to making your attack against some other character... occupying the square B. Normally, this will rather seriously limit your options down to "none".

I believe, however, that the object will still be destroyed, so at least you are handing out hindering terrain to an opposing figure.