They're installed by running their respective payloads. I like briccmii's implementation the most because it actually can tell you if AutoRCM is installed or not unlike the other two. As for battery drain, I haven't personally tested it but theoretically there should be no increased battery drainage between the 3 of them, even compared to a console without AutoRCM. That is because AutoRCM affects the bootloader of the console which is only the power-up process of the Switch aka it should have no bearing on the console once its already on. Of course, people are free to submit their own anecdotal evidence some do drain more than others but there's too many factors to consider if there's truth behind their stories.
One interesting thing that did come up was that I saw a thread that showed SX OS drained more battery than other CFWs (has nothing to do with AutoRCM). I'll see if I can dig that one up.