A similar question was asked on the cooking stack exchange quite a few years back. The answers and comments there mostly address your first and third points.
It seems that there's consensus that bubble formation differs between instant and brewed. However, I assume from your comment that both your decaf and regular were instant. There may still be differences in the bubbles. From Wayfaring Stranger on the Cooking SE:
Coffee foam/bubbles is made up of a mixture of proteins, sugars, oil droplets, caffeine etc, and the lifetime of a bubble is highly dependent on the composition of its membrane. Given that decaf is coffee that's been solvent extracted, it wouldn't be at all surprising to see its different composition affecting bubble lifetime. However, no one seems to have conducted definitive studies of the matter.
There's a variety of caffeine testing strips that might be worth investing in if you're routinely serving coffee to someone who's sensitive to caffeine, but I wouldn't know how feasible it'd be to craft your own alternative with some at-home chemistry.