How much of this travel will be booked on an underlying cash fare, and how much will be booked with an underlying Avios fare? (Before upgrades, etc. are applied).

If it's an underlying Avios fare, it'll be BA only.

A TA will only be helpful in getting availability, e.g., if you book a business cash fare and use a GUF2 to upgrade into a revenue A fare after you've exhausted avios availability.