Are I and J vectors necessarily one unit on the positive semi-axis of X and one unit on the positive semi-axis of Y on the exponential axis?

I and j vectors are generally only used to represent unit vectors, and when solving problems, they will explain the problems, just as solving equations generally uses X and Y to represent unknowns.

Is it true that a vector =5i vector +2j vector = (5,2)?

The same is true in the plane rectangular coordinate system.

A (0,2) is equivalent to OA = (0,2)?

It is equivalent, but OA has to draw an arrow on it to indicate that it is a vector.

O Must it be (0,0)?

It's usually like this. When you do the problem, the general questions will be explained. Don't say, you can also default to the origin.