Appearing and Disappearing Same Object at different positions

Unless you are wanting the object to appear at random locations as Jose described this is pretty basic stuff.

Just keyframe the layers opacity to zero, then keyframe it's position to the new place and then keyframe the opacity back on.  As Jose said you'll have to put holds on the keyframes so they don't drift the next position.  Do this by right clicking on the keyframe and selecting it from the context menu. You could also manually hold the position by adding two key frames for each position: one for the position it stops at and then second keyframe at the same position for when starts moving again.

Repeat.

Or if it will work with popping on and off frame to frame you can just duplicate the layer put the different duplicates in the places you want them and then trim the layers so they appear and disappear when you want.