Thank you Nir!
(1) According to their web site, they last for 2–3 weeks if you configure them to as an iBeacon. So if you fly frequently and get one of these beacons, you probably want to travel with a spare CR2032 battery just in case.
(2) Actually, I didn’t pay any special attention to the beacon when I packed, so it was probably somewhere between my clothes. I believe that as long as you don’t have any large metallic objects or big liquid containers (Bluetooth energy is absorbed by water) next to the beacon, you should be fine.
As for the range — In my case, I got the notification about 15 seconds before I actually spotted my suitcase. It really depends on the transmission power (more power means shorter battery life), but you should be able to get a range of about 50–70 meters in the open air (and about four times this number once Bluetooth 5 beacons will be available for purchase).