Is my radio pulling more current than it should?
You're using a 12V supply on a system that needs 13.5V. It says 10% tolerance, but that is still 12.15V minimum input or 14.85 maximum input. Depending on your DC source you may be able to tweak that up a little bit.

Anyway, the given current consumption is for 13.5V. So 13.5V at 19A is roughly 256W. 256W at 12V is 21.3A. This means that for a 100W output you're drawing 21.3 A instead of 19A. So yes, you need a larger fuse or a higher voltage supply. Do not use the 24V supply though!

To answer your other question, yes. Power in is always greater than power out because of efficiency. Couldn't find a datasheet for the product you listed so I can't give an exact number.