What is the evidence for the scholars' permissibility of intending separation during prayer, and can this be analogized to "And when you are among them and lead them in prayer..."? And does the traveler pray three rak'ahs and make the taslim with the imam if he joins in the second rak'ah with the intention of 'Isha prayer?

If the worshiper prays a prayer with fewer rak'ahs than the Imam, such as praying Maghrib behind someone praying 'Isha', it is permissible according to the preponderant opinion, and the difference in intention between them does not matter. After the worshiper completes the rak'ahs of his prayer, he has the choice between leaving the Imam and performing the tasleem or waiting for the Imam to perform tasleem with him, and waiting is better. As for the permissibility of leaving the Imam, whether for an excuse or without one, scholars have differed; some permit it absolutely, some permit it only for an excuse, and some do not permit it at all. If the worshiper joins the Imam in 'Isha' prayer with the intention of Maghrib, and he is with the Imam in the second rak'ah, he should perform tasleem with the Imam because he would have completed his prayer. However, if he joins with the intention of 'Isha', he must perform one rak'ah after the Imam's tasleem.