We also know there is a drop in amplitude roughly corresponding to 1/h, where h = harmonic.
Even qualified by the word 'roughly', I'm not sure how useful that is as rule of thumb. Some waveforms (e.g. a sawtooth wave) have that property, but many waveforms that can be produced both by real and electronic instruments have different relative strengths of their harmonics. Also, the relative strengths typically vary over time, according to playing technique, and so on.
So if 440 is our fundamental, 880 is our second harmonic. Does this mean the amplitude of the second harmonic =440 (880*1/2), or =220 (440*1/2)?
I think you are mixing up amplitude with frequency. If Your first Harmonic has a frequency of 440, the second harmonic has a frequency (not amplitude) of 880.
If assume that we have a sawtooth wave, so the relative amplitudes of harmonics are 1/harmonic number, and we assume that the amplitude of a fundamental at 440Hz is 1 (in some arbitrary unit), then we'd have
amplitude of 2nd harmonic = 1 * (1/2) = 0.5
amplitude of 3rd harmonic = 1 * (1/3) = 0.333...
amplitude of 4th harmonic = 1 * (1/4) = 0.25
and so on.
As the human ear can hear from 20hz > 20,000hz, if the former is true, it would mean in this instance we can hear up to the 46th harmonic (440*46 = 20,240), however if the latter is true, it suggests we can hear only up to the 22nd harmonic (440*1/22 = 20).
Again, we have to be careful not to mix up frequency with amplitude.
A simple way to calculate the highest harmonic you can hear is
20 000 / (fundamental frequency of note)
If your note is at 440 Hz, then 20 000 / 440 = 45.45.... so simplistically speaking, it's true that you can in theory hear up to the 45th or 46th harmonic for a note at 440Hz. For lower notes, you might be able to hear higher harmonics. But remember that all this depends on how loud the harmonics are. The human ear is less sensitive at very high frequencies, so if the amplitude of the harmonic were only 1/46th of that of the fundamental, it might be hard to hear.