If supply amperage is higher than max. amperage, do I need a resistor?
To the first order...
You are correct. The load controls the maximum current that may flow, while the source controls the maximum voltage available.
but...
You are not correct about your LED. That's a different problem. Your thinking assumes, Ohm's law which assumes linear (and in-phase) operation.
Diodes (including LED's) are non-linear devices. The Diode will present a constant voltage (approximately) when it is &quot;on&quot; independent of the amount of current flowing through it. The LED will be brighter with more current and burn-up (be destroyed) if too much current is allowed to flow through it for too long.
Notice how the line to the right of the y-axis in the figure is almost vertical. That implies that the voltage will change very little if the current through the diode changes a lot. V clearly does not equal IR for a diode.

Most discrete LED's in the microcontroller world hover around 2V at 20mA (varies by size, chemistry, and construction of the LED). If your microcontroller provides a 3.3V output through one of its general purpose pins (GPIO), then the current the LED demands from the circuit will exceed what the microcontroller can provide through its output pin and the internal resistance of the output driver in the microcontroller will limit the current to its maximum.
This will ultimately destroy the output driver of the microcontroller. To prevent this, a series resistor is added to limit the current explicitly to something safe.
You work backwards to size the resistor: (Vcc - Vled) / Iled = R
In most 3.3V microcontroller applications, the value turns out around 100 Ohms.