Microcontrollers and custom boards
Question 1 and 3

Microcontrollers are CPUs that have special pins dedicated to electronic communication. The most basic unit is GPIO (General-purpose input/output). It allows you to program a pin as an input or an output. 

As an output, you can set it to LOW or HIGH (0 or 1). A high output corresponds to a voltage of VCC, which is usually 5V or 3.3V. A low output corresponds to ground or 0V. You can think of each pin as a small battery that can be turned on or off.

As an input, you can read the voltage level. If the voltage is near VCC then the readout will be HIGH (1) and if it is near ground it will be LOW (0). 

Though this sound fairly limiting, there are lots of circuits, ICs and breakout boards that communicate using this setup. In fact, this is the basis of Digital Electronics, which is a huge and exciting subject on its own.

I'm including here two basic circuits that should get you going. The first is how to connect an LED to an output GPIO pin, and the second is a pull-down push-button connected to an input GPIO pin. 







simulate this circuit &ndash; Schematic created using CircuitLab

You also asked about what happens if you need to drive lots of LEDs. Recall that the GPIO pins can be thought of as tiny batteries. If you have many LEDs it can become too much for the pins (to much current required). If so, you might need to use transistors as switching "helpers". 

Hopefully, this should give you something to get started.

Question 2

The USB protocol is unfortunately a little complicated. Some micro-controllers don't even support it at all. These are advanced subjects that is probably better answered in a book or some more in-depth material.

In General

To get started, I would recommend going through the Arduino books and examples. These are great in terms of teaching and you can quickly get to a point where you can make interesting projects.