Regarding the ki abilities Object Motion and Mass Movement, it says the object must be within sight or that the character must be definitely aware of where it is. Does anyone attach a distance limit to that? Does it work through a telescope?

It says the use of this ability costs an amount of ki per turn. Do you treat that as meaning a person can keep the object levitating over the course of several turns? Or is he picking it up and setting it down each turn?

Finally, how far can you move it in a round's time? The character projects his energy as an extension of his own body to touch and move objects. Do you treat that as though it can only move as far as you could throw it were you actually touching it?

Sorry but there are no official rules for this.

It says the use of this ability costs an amount of ki per turn. Do you treat that as meaning a person can keep the object levitating over the course of several turns? Or is he picking it up and setting it down each turn?

Personally I would say that means you can maintain it, almost every other ki ability that has a per turn cost is capable of being maintained so I don't see any reason why this one should be any different.

As for the rest the GM will have to decide what his official stance on it will be.