Benford's Law really only applies to numbers where the growth rate is a function of the current value (ie. exponential growth). It's not some magic property that can be applied to any dataset.
This isn't true. Benford's law applies just as equally to ordinary, arithmetic growth as well. The reason Benford's law works is because a growing number spends as much time with "1" as its initial digit as it did traversing the entire previous order of magnitude. This is true true whether the growth is exponential or arithmetic or multiplicative.
Consider a sequence increasing by 1 each period. Now pick a random number between 1 and 10000. Generate the sequence between 1 and your random number. It will approximately conform to Benford's law, modulo your ending number.
Benford's law is a property of growing numbers, not of any particular kind of growth.
Linearly growing sequences don't follow Benford's law, but lower first digits (1, 2, 3) are still more probable than higher first digits (7, 8, 9) "most of the time", as you describe it.
That is not true, you just happened to choose lucky starting numbers. For example consider this one: choose a number between 1 and 10000. Generate the sequence between 9000000 and 9000000+(your number). Everything starts with 9.
Benfords law applies only to exponential growth over a long timescale.