There is no master account in BPM that you can use to view every task, instance using the REST API. The account using the REST API must have permission to view the task either by having worked on it, or being in a group that the task is assigned. At the moment, the REST API does not support the use case of using Administrative/Call Center apps out of the box where a user/manager needs to see everything in 8.0.x.
For task reassignment, by default the tw_admins group can reassign tasks using the REST API/JS API. However, you can add additional groups by overriding the 99Local.xml file.
You can refer to the following thread. Using JS API, its straight forward to reassign and this you can define inside the task. Also you can expose this task as startable service so that it can be accessed via REST API (under Service API) itself.