I cannot speak for the fast line followers you are referring to that prefer using the QTR-8A, but we generally recommend the QTR-8RC. You can find some details of the benefits of using the digital QTR sensors in my post in this thread.
The benefit you quoted from the product page about the improved sensitivity is referring to the voltage divider used on the analog version of the sensor array. Each phototransistor on the array is connected to a pull-up resistor to form a voltage divider that produces an analog voltage output between 0 V and VIN (which is typically 5 V) as a function of the reflected IR. When using a microcontroller with a 10-bit ADC like an Arduino, this limits the reading to 1024 values, whereas the QTR-8RC sensors work by measuring how long it takes the output voltage to decay due to the integrated phototransistor.
The 5V regulator on the A-Star 32U4 Micro can output around 100mA; however, about 25mA is used by the board itself. These reflectance sensors can also draw current in bursts, so it is probably best to power it from a different 5V source.
If you are using all 8 of the sensors on the QTR-8RC reflectance sensor array, you will need to use 8 digital I/O pins (one for each sensor). Additionally, the QTR-8RC reflectance array allows you to optionally control the IR LEDs, so you can use one additional digital signal to control the LEDs through the LEDON pin on the board.
As for your last question, it sounds like you are asking how the sensor works. To use the QTR-RC sensors, you will need to first drive the sensor output high, which can generally be thought of as "charging the output node". Then, with the output node charged, you can remove the voltage on the sensor output and monitor the output. When the voltage is removed from the sensor output, the voltage on this output will start to drop; this can be thought of as "discharging the output node". The time that it will take to fully "discharge the output node" depends on the phototransistor's resistance, which depends on the IR reflectance being measured. This means that by measuring how long it takes to "discharge the output node" will allow you to determine how much reflected IR light was measured. More details about how this works can be found in the "How it works in detail" section of the QTR-1RC product page.