Newbie Assistance - Understanding Fairy Lights
1: About right, but detailed values depends on the LED.
2: No, Arduino pins can't output 20-30 mA safely. It exceeds the nominal operating conditions. If it is a 5V device with Mega328P, it is 20mA tops per pin. And there is a total safe limit too, max 200mA per chip, but also different ratings for sinking and sourcing currents, and some limits for various groups of pins, so by keeping total curret below 100mA per chip, it will be within limits.
3; No, the batteries are in series, so if a single battery can provide 50mA at 1.5V, the pack of them can provide 4x1.5V=6V at 50mA, just at a higher voltage than a single battery. If the batteries are in parallel, then it is a 1.5V 200mA. If the batteriy pack can also be arranged into pack that can output 100mA at 3V. Parallel batteries are usually avoided though.
4: Sometimes they also have an electronic chip and circuitry to convert voltages, not just simple resistors.