OK, I've found a tape measure and a piece of wood. The height above ground at the front of the passenger seat of my Crosstar is about 23" / 58cm. The front of the driver's seat (which is at or close to maximum height adjustment) is 24". Note, however, that the seats aren't flat (see photo) so that where you sit is lower than these measurements. I would note that I've found that, while driving, I had too much weight resting on my thighs and had to invest in a wedge-shaped cushion. Seats in the Jazz are higher than in most cars and the Crosstar is higher again. Another feature of the Jazz design is that the doors (parking space permitting) open wider than many cars to make it easier for entry and exit.
The Crosstar's ride quality is, I believe, better than the normal Jazz as the extra vehicle height enables longer travel suspension. The Crosstar rides better than the HR-V which I owned previously.
If your driving style is relaxed then you'll rarely hear the engine but if you drive more aggressively or find some steep hills to go up which demand more power from the engine then it becomes audible. It probably gets noisier if worked even harder but I've never needed to explore that situation but I'm not a press reviewer.
The cabin heater uses the engine heat which, in cold conditions, will cause the engine to run more of the time (I would have configured the electrically-powered aircon to also work as a heat pump but, unfortunately, Honda's designers didn't ask for my input). If the engine is cold then it always comes on at the start of a journey to warm itself up to some extent but how long it runs for is affected by the cabin heating demand. In some situations turning the heater fan off will result in the car switching to EV mode. Having the cabin heating off isn't such a hardship as the front seats have electric heating.
Cold start plus full battery is a rare condition as the vehicle normally switches to EV mode once the battery charge reaches 70%. The remaining battery capacity appears to be a reserve for regenerative braking when going down a long hill. We need someone who lives at the bottom of such a hill to tell us what happens when starting with a cold engine.