That Ciao! should be just fine, compressor or not. Since they're planning to go direct from the Ciao's outs to the A/D, it would probably be better to apply a VST to the incoming signal in the DAW itself. That way, it's possible to futz around with compressor topologies, which may be necessary for different patches. For example, with sounds that tend toward percussives, you'd want to do some basic compression to mash that a bit and keep the peaks under control, but if you're wanting to slam the hell out of a source, then using a VST clone of an 1176 with the "four-button trick" would be perfect.
As for using TRS 1/4" to 3.5mm, that's a decent plan, but MAKE SURE not to try and do this with 3.5mm - 3.5mm TRS cables because, invariably, they'll get in with the rest of your patchcords and then when you NEED them, well... But at a pinch, you could use unbalanced TS cables, but that's sort of a kludge with certain drawbacks of its own. But as for the headphone-to-modular preamp idea...don't. Headphone signals are hotter than line-level, which is what the Ladik's expecting. A better idea for getting the Hydra in with other signals would be to run a small stereo mixer, connect all of the toys you want to run through the modular on that, then send the mixer's out to the Ladik inputs. Convenient and simple!