Disappear is obviously a really quick denial to someone using premature or call of the haunted. But if they select the target and I chain disappear, can they just select a new target for their revival since that option was removed before the effect completed? Or does removing that monster render their card useless?

If im not mistakin Premature Burial and Call of the Haunted would "disappear" too because their target is no longer in the graveyard.

Cards that select a target upon activation (such as Premature Burial, Call of the Haunted, Light and Darkness Dragon, etc.) do not get to choose a new target if Disappear removes the targetted monster. What happens after that differs from card to card, however (LaDD will still destroy everything you control, for example).