The control pins of servo motors do not take a huge amount of current. The current draw specified for the servos is for the motor itself which doesn't come from the GPIO I/O pins and so doesn't count in the 16mA limit.
You would probably be able to connect the servos to a Pi3's GPIO pins and power them through the Pi, but that's a maximum of 1.5A and a noisy signal with possible back-EMF. It's not a great idea; it could crash or even break the Pi.
A pi can certainly control one micro servo directly from the GPIO pins -- I've done it -- but I don't know what the maximum number of servos would be. I cannot find anywhere that says how much current a servo requires on its control pin, but I found one place (https://www.pololu.com/blog/17/servo-co ... -in-detail
) that recommends 220 ohms in series as protection. That would suggest a maximum current of 5/220 = 23mA but I imagine the minimum is much lower than that. The only way to find out appears to be to test it. You would have to measure the voltage drop over that resistor using a dual-channel oscilloscope.
As for the power supply, it needs lower than 7.4V. Ideal would be 5V. At the very least the servos and Pi should be connected to the supply individually and you may need to have two separate supplies for the servos and the Pi. (In which case you join just the grounds together.)
Read that link though; there's a lot of useful information there.