Unattended fires certainly are a concern and you're wise to raise to the issue. Here are the basic action items (as I see it) to help set your mind at ease prior to unattended burning (especially while sleeping at night): Most of this is good . . . a few technical points to address though.
1. Ensure your new stove is installed properly and to manufacturer's specification. +1 . . . and there is nothing wrong with exceeding those minimum standards . . . gives me a real good peace of mind.
2. Learn how to throttle the fire down by restricting airflow into the firebox before going in for the night. This lowers the temperature and makes it less likely an event will occur at night while you're sleeping. Most flue-pipe fires start when the flue is dirty and there is a raging fire/high temperature operation. Even with a dirty flue, a simmering fire is unlikely to ignite it. Make sure everyone who uses the fireplace/stove is educated on how tro properly operate it. Yes and no . . . modern EPA stoves don't really throttle down . . . and in fact reducing the air to the point before the fire stalls will typically result in a very strong Bowels of Hell in the Woodstove Effect . . . but the temp in the chimney should not be especially high . . . more to the point . . . burning at the proper temps for the stove and chimney will help prevent excess cresote build up . . . and educating folks as stated to how to run the stove properly is good.
3. Keep your flue pipe CLEAN and properly serviced every year. Have it video inspected once a year to ensure nothing has gone wrong since last season. Know its condition every year before using the unit. +1 . . . but an even better idea is to regularly inspect and clean the chimney throughout the burning season. I am a bit overly ambitious and check and clean monthly . . . most folks clean at the start and somewhere in the middle of the burning season.
4. Properly seasoned, dry wood will help keep the flue clean and make chimney fires much less likely. +1 . . . along with also burning at the proper temps -- not too cold and not too hot.
5. Ensure you have several smoke detectors with fresh batteries located throughout the house in logical locations. Check/replace batteries frequently. +1 . . . logical locations being in the bedrooms, hallway and every level of the house . . . you can go overboard and put them in areas where you may end up with many false alarms and after a while the family will hear the detector and just assume it is false. Bad locations include kitchens, too close to the heating appliance, bathrooms, garages, etc. Also, battery technology is such that just changing them once a year is good . . . but remember to also change out the entire detector every 10 years.
6. Keep a CO detector in your bedroom (and kids room if you have them). I position my CO detector down low at head level so that it detects CO at an elevation I'm breathing instead of on the ceiling. This may not be necessary, but I do it just in case. +1 . . . CO when warm rises, but it quickly reaches room temp and can be found at all levels. It doesn't hurt or help to put the CO detector at the level you are breathing . . .
7. Do the obvious: remove flammable materials from around the fireplace. Visualize what would happen if a log settled/shifted in the fireplace at night and possibly attempted to roll out of the grate/firebox. Make whatever precautions it takes to prevent it from happening. Ensure the latch mechanism and grating are sufficient to prevent it. Don't pile logs up in a way that promotes a "logalanche" as the fire burns down. +1 . . . the "glass" -- actually neoceram is pretty tough stuff . . . most of the stories we hear about the glass breaking is when folks jam a split in and then attempt to forcibly shut the door. That said, I like to err on the side of caution and try to stack the load so it will tend to fall down away from the glass . . . but if some hit the glass it's typically not a problem.
8. One of the most common areas a fire starts with stoves/ZC fireplaces is at the throat of the stove where the flue emanates from the firebox. Fire can emerge from here if there is a flue-pipe fire and the metal flange is overheated and distorted (where the seal integrity is lost). I've strongly considered mounting a temperature probe array in this area to detect this situation and provide a pre-emptive audible warning that a breach has taken place well before the rest of the house is burning. Otherwise you have to wait for smoke to reach the detectors. By then it's often too late - for the house at least.
9. Keep a decent sized fire extinguisher on hand. Make sure everyone knows where it's at and how/when to use it. +1
10. Remember in school when you were taught to "have a plan" in preparartion for a house fire? The same is true today, it's not just a corny educational film after all. Make sure everyone knows what to do in the event there is a fire. Where to meet, where to go, what number(s) to call to get the fire dept there ASAP. Not to go back into the house after getting out (you'd be amazed at how many get killed doing this simple thing). Explain that the house becomes a deadly gas chanmber filled with invisible poisonous gases once plastics/synthetics start burning. It can and will bring you down, so get OUT when there is a fire. There are other considerations too. For instance, in my bedroom the windows were sticky and difficult to open. My girlfriend couldn't open them because they were sticky, ill adjusted and the latch system was non-intuitive. You couldnt tell which latch position was open. And since the windows were sticky, even with them properly unlocked, they still appeared to be locked. In a panic, this is absolutely deadly. Also, even if the windows were opened, there was metallic debris below that would have injured anyone jumping out of them at night (or during the day). All of these interfering factors must be recognized and remedied - especially where children are considered! Install esxcape ladders where necessary. Practice at night for realism - make it second nature. Practice escape plans and remove ALL obstacles. Do dry runs until they are second nature. +1 . . . always have said having working smoke detectors without an escape plan in place is like having a new Corvette without an engine . . . it looks good, but it's not gonna get you where you want to be.
Those are my 10 basic remedial factors that help me sleep at night right before I turn down the fire before turning in.