In order for a task to be tied to a customer, that task has to belong to a project. It is the project object that is tied to customers, and the task will inherit that customer (or set of customers). So you cannot link customers to to-do tasks without substantial customization (mostly on the reporting side).
As for the stopwatch, you need to set "actual effort updated from timesheet" to true in order for the task to pull the actual effort from approved timesheet information. If this is set to true at the project level, it will roll down to every item in the project. There is also a system setting in Time Tracking (10.1) that will set this automatically for all new projects.