OBR DH question

[newump]

DH in the 4 slot, batting for F1, Smith. While on Defense, Smith moves to RF. Does Smith now bat in the spot of the original RF?
Is the DH terminated at this point? And does the new F1 now bat in the old DH slot??

Second sit: DH enters the game to pitch. DH obviously stays in the same slot. original F1 moves to RF and then bats in the spot vacated by RF. DH is terminated?

Thanks,
G