I suspect that teleportal stone is the one needed for your quest. However, if you mean by "right one," is it a teleportal stone you can keep for personal transportation--then, no. You find a pair of those in Act II. <img src="/ubbthreads/images/graemlins/smile.gif" alt="" />
And yes, you can go back and forth between the "real world" and the battlefield at any time. There are no restrictions. You can even leave items on the ground, there. Just make sure you pick them up before completing each act, since a new battlefield is generated when the next act starts. Anything left in the old one will be destroyed.