is is possible to drop voltage without knowing a components amperage
No need for a voltage dropper with two resistors. Just assume (a fairly accurate assumption I might add) that, the LED has 2.1 volts across it then, put a resistor in series with it to the 9 volt rail. The value of the resistor sets the current: -
$$I = \dfrac{\text{9 volts - 2.1 volts}}{R} = \dfrac{6.9}{R} = \text{20 mA}$$
Rearrange to find R (it equals 345 ohms).

Wouldn't a circuit like this drain a battery or cause the circuit to
short out?

It's extremely sub-optimal.

If i started with 9V. Could i drop the voltage down for a component
that takes 5V without knowing how many amps it uses?

You could (and waste a lot of power) or, just use a voltage regulator - that is what they are for.