as to signal merging, dunno, I suspect it might be effect by effect.
for instance, I expect a reverb alg to have some cross-feeding so you get a stereo image just with the point sources in different places.

Other effects I expect are processed independently to maintain separation (but with the same settings)

so the long and the short -- it's not the total dual mono separation a lot of stickist are interested in.
but at the pricepoint and footprint -- 2 certainly isn't a deal breaker

It has two instrument inputs... can you apply different effects to each signal? Or are the two signals merged internally and everything then applied to both?

The latter. If you want different effects on each side, you'll need another pedal. The two inputs are electrically separate, meaning you can use both without the bass and melody sides fighting with each other as with a Y cable. But the digital processing after the input stage is unified. The stereo outs are for effects like ping-pong delay and stereo modulation.

Hmm...I bought an HP4 for my current band and never thought to use it for Stick practice. I'll have to do that!
I bought a Behringer cheapo $25 headphone amp just to have something very small to bring to Free Hands Academy 2 years ago. It's small, and you can play Stick via headphones. But the sound leaves a LOT to be desired, and the signal is extremely weak if you try to use a 1/4" line in. (It works well with an XLR 3-pin microphone input.)