LEDs

CAP1 is a power pin as shown and you describe from your reading, perhaps it should have been listed as such. However it is not intended to provide any specified current or be used elsewhere in the circuit design. The LED reference is an exception.

Q1. It is an input of the capacitance to the internal regulator circuit. Do not apply a voltage or any significant load to the pin.

Q2. The patterns are options. The size of the transistor may be required for power dissipation. With 5 LEDs the current will still be low but the power will be more significant. People like really small transistors so the SOT23 pattern is there as an option. It might be suitable at low voltages and few LEDs. If you exceed the power of the transistor it will likely short providing battery voltage to the CAP1 pin damaging the AFE. When selecting the transistor be sure it will handle the voltage, the power, the current and have a high hFE so the current load on the CAP1 pin is very small. A hFE >100 is desirable. If you have an efficient 3.3V available in your battery that could be used to power the LEDs that would be great.

Q3. The LED pins are controlled current sinks in LED mode. As LCD pins they are open drain pull downs. If not used they can be tied to gnd or left open.