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The others have their set-ups on standby in case one of the 21 is unable to produce a block or gets voted out. At least that's my general understanding.

My understanding in Steem is, instead of 21 full time BP's, there are 20 with the standby's rotated in to slot 21. https://steemit.com/faq.html#What_are_Steem_witnesses

I'm not exactly sure if they have to run a server. I wonder if there would be a way to know whether or not if they run one besides having the up-to-date blockchain but that doesn't mean their server would have the required power to produce a block.

To answer your second question, I think it's a question of efficiency and might also be tied to the fact that backup BP might not have to run a server.

I think Steem would benefit from having the witness be paid proportional to their amount of votes, not just so for the backup witnesses as it is now. This would create more competition among the top 20.