One of the things that your Mac needs to do after the upgrade is indexing. Basically it trawls through the stuff on your drive to create an index for Spotlight to use when you want to look something up. This is most likely what is causing the increase in power use, but keep an eye on things. It should go down after a while.
As for the search, Apple introduced a feature on iPhones a while ago that enabled text on images to be recognised. What you're seeing now is basically that feature, expanded a bit, rolled out to the Mac as well. As far as I know it uses the processing power of your own computer to recognise text and other features on images. This is something internal to your system and not shared with Apple's or anyone else's servers.
The feature you mentioned was (IIRC) about images shared to Apple's servers through iCloud and as you say, it was not taken up. To my knowledge, Apple is still the most trustworthy of the large media/internet/technology firms and the one most concerned about privacy. If you want to make sure about this, the best way is to sit down and have a good read of the terms of service for both your phone, your Mac and the iCloud services but don't blame me if they put you to sleep!
