When picking up an object can u pick up an object that is adjacent to u? Do u have to move into the square the object is setting?

To pick it up you need to be adjacent and still have movement left. So if you were next to it, but had already used all your move, you could not pick it up.
Also, if you are forced to stop because of an opposing fig, you could not pick it up eigher.
Was that clear enough?

This is not correct.

If I have a speed of 10 and am in my 10th square, I can still pick up an object.



But to answer the op's question, yes, you need only be adjacent. (Actually, if you don't ignore hindering terrain and have moved into a square with an object, your movement would have stopped, preventing you from picking up the object in your square.)

If I have hypersonic speed and move past an object can I pick it up as part of my move action even if it was several squares away to begin with?

yes u do not need to start or stop adjacent to the object just move past it.

As long as the path of your movement passes through a square adjacent to the object, you can pick it up.