web farm scheduled tasks

Unless you specifically want the scheduled task to run on one or some of the servers in the farm, there's no need to specify which server they will be executed from. We have several clients with 2 or more servers in their farm and have only ever once determined we needed to assign a server name to a given task. That was back in v7 and v8. The scheduled task code will never be executed on the MVC site because it needs the CMS to be able to execute that code. Hopefully this helps.

In general, you need to clone scheduled task to run on each server if the scheduled task is working with the file system - e.g. working with search indexes and so on. So, the job is done on all file systems. Other tasks, working with DB objects - it does not matter on what machine the task is executed. It is explained in the documentation on configuring web farms.

Makes sense. So with each .net core site on the same server as the each admin, we only need to duplicate the tasks once.

Just to be sure - it does not matter whether the whether the apps are on the same physical server or not. Each app is working only with its "root directory". So, if you have e.g. two admin apps in a web farm and if they are on the same physical server, you still need to clone the scheduled task for each app instance.