How would I provide power to these devices? Can I power them using batteries? If so, where can I buy them, and approximately how much do they cost? Also – do I need to buy any additional hardware to be able to power the devices using batteries? And what kind of battery life can I expect based on the type of battery that’s recommended?
Yes, you can power the devices by batteries. However, gateway and repeaters have to be on all the time, so it’s only practical to power them by USB power adapters, computers, etc…
All of the devices have a JST-PH battery connector for a 3.7V LiPo battery, same as the Electron. Only the Boron 2G/3G includes a battery, however. All others you will have to purchase one separately.
All of the 3.7V LiPo batteries at Adafruit are compatible, and are available in sizes up to 6600 mAh.
There is a charger built into the devices that will charge the battery when powered by USB.
It’s too early to say the exact battery life, and it really depends on a lot of factors. Using a Xenon that only wakes up for a second every 15 minutes would probably run for months. An Argon running full speed, maybe a day or two, using a 1800 mAh battery.
Can these particle mesh devices be used as WIFI repeaters at all? If so, what kind of bandwith and/or reliability should I expect? And is there a limit as to how far out I can expand the mesh network until the performance degrades to a point on unusability?
No, they cannot be used as a Wi-Fi repeater. And the mesh network is low-bandwidth. You should only expect to get the low 10s of Kbytes per second. It’s not intended for high-bandwidth usage. The exact numbers have not been determined and will vary depending on the number of hops in the mesh as well.