During the day, my Eupolyphaga roaches stay hidden in the substrate. However at dusk and during the night the adults are relatively active. The males tend to wander around and will escape if the lid isn't closed well (happened here).
Compared to Polyphaga roaches I find them much more active. They are however shy and will dig if disturbed. If you pick them up, they often play 'death'.
As 'All about insects' and 'Roach collector' mentioned, they eat leaves and eat quite a lot of additional food. I feed mine gold fish food in addition to the substrate leaves.
They do prefer more moisture than most Polyphaga species. I keep half of the container moist. I use a substrate of coconut coir mixed with partly rotten oak leaves. My roaches mainly reside in the moist part of the enclosure.
They are produce a lot of ootheca, which hatch relatively fast if you keep the temperature high (4-6 weeks at 30°C-32°C/ 86°F-90°F) .