They generally have about a 75ft sensing range and can be additionally equipped with external battery and solar charger, so no AC power required.  

I immediately changed the battery (it was overdue) but it continued to beep.

Or their phone battery is dead?

You go and figure out the batteries in the thermostat are dead.  

So take that in for just a moment and than lets fast forward to a few months later to November when GM pulls a rabbit out of a Detroit hat and does a 180 and announces it will not shut down their historic Hamtramck plant but rather dust it off in preparation to unload a spanking 3 BILLION DOLLARS into it to begin building electric pickups, vans, battery modules, and possibly even reviving the Hummer brand there.

I don't have a complete list for you... but a couple of really handy ones are a Saws-All , and a battery powered Crown Stapler.  

The mentorships are mainly online modules.  

Make sure stair railings are secure, stair treads are in good shape and that all smoke detectors and CO detectors have a new battery and are working.

While that is absolutely no substitute for a battery of surveys (soils, etc) performed by the appropriate engineers, it can help get you a basic idea about the property and what kind of work might be necessary.  

For example recently I had two and these are their charges:PERSON AAGG ASSAULTW/ DEADLY WEAPON WITHOUT INTENT TO KILLTOUCH OR STRIKE/BATTERY/DATING VIOLPERSON BCORRUPT BY THREAT PUBLIC SERVANT OR FAMILYDUI ALCOHOL OR DRUGS 1ST OFFENSERESIST OFFICER-OBSTRUCT WITHOUT VIOLENCEThis is before viewing the apartment, before actual application.