How can I bill by Fees per Task when each team member has a different rate?
Project setup doesn't allow for combining two types of hourly rates, so there's not a built-in way to bill a project by both person and task.
If you need this kind of granularity, you can set up your project's Hourly Rates to use Task Hourly Rate. Then, you can create separate tasks for each of your specific team members' different rates. You'll want to name these clearly so that your team members can accurately track their time.
For example, you could create a task called "Jane Programming" with an hourly rate of $200, a task called "Jane Research" with an hourly rate of $150, a task called "John Programming" with an hourly rate of $175, a task called "John Research" with an hourly rate of $125, and so on.
In this example, Jane and John would track their time to their own designated tasks within the project. That way, when it comes time to invoice, you can essentially bill your client by each person's individual task rate.