If I have a battery that provides a high current at almost constant voltage, how do I use it to power other components that require lower currents?
From your question it appears in addition to powering the drone, you also need to power an RPi and a transmitter.

The transmitter requires 12V so the 11.1V battery may not have sufficient voltage. You should check the transmitter functions correctly with this battery.

The RPi will need a 5V supply so I suggest you use a simple voltage regulator (LM7805) or a buck converter (something like https://www.amazon.com/dp/B076P4C42B?tag=duckduckgo-ffab-20&amp;linkCode=osi&amp;th=1&amp;psc=1) to drop the 11.1V from the battery. The Rpi will likely need 500-800 mA (see https://raspi.tv/2018/how-much-power-does-raspberry-pi-3b-use-power-measurements for a rough idea).

Your question does not seem to imply any interconnection between the transmitter and the Rpi so I have considered them independently above.

I would test this all on the ground (remove the props) to check it works safely and get a baseline for the flying time. The RPi is using a substantial part of your current budget.