Electronic – Can a DC regulator reduce/step down DC voltage

Arduino Leonardo, like the Uno, uses an NCP1117 linear regulator (LDO), which can supply 800 mA, but at 11.1 V input that would be 4.88 W, so thermal protection will set in much earlier.

Using USB is a possible solution, but keep in mind that USB doesn't have to supply more than 100 mA, you'll have to negotiate for 500 mA. And Arduino is not designed for low-power, I don't know what the Leonardo consumes, but I guesstimate the Uno's supply current at 50 mA, so powered from USB that may leave too little for for instance a series of LEDs.

Your own switching power supply looks like the best solution. Bypass the NCP1117 and supply it directly with 5 V. A 12 V to 5 V buck converter should be able to have a near 90 % efficiency. If the dingus would need 50 mA it can run for more than 48 hours on the LiPo battery.

Further information
Arduino Leonardo schematic

If you take the input for the 7805 from the 7809 output, you must include the current drawn from the 7805 into account when determining the power dissipation in the 7809.

You should not use a voltage divider to make 3.3 volts - the voltage on your 3.3 volt line will vary depending on the current drawn from the 3.3 volt line, as that current will have to flow through the "top" resistor of the divider, increasing the voltage drop across it. Look for a dedicated 3.3 volt regulator, or use an LM317 or similar adjustable regulator.

Depending on the currents you need from each supply, it may be best to use a switching regulator to get from the 15 volt supply to 5 volts.

Make sure you have adequate heatsinks on the linear regulators!!