First, just what is KMS-R@1n.exe?
If you are using a "cracked"; i.e. illegal version, of the Windows OS or any other legit Microsoft software, removal of KMS components will cause all licenses associated with them to become invalid. If all your software licenses are legit paid ones from the software manufacturer, then there is no reason for KMS associated components to remain on your PC.
This situation is also a classic example of why Eset does not enable the potentially unwanted software option by default. Eset's stance to date is they are not the "software license police." The previous said, using of cracked software these days is a risky undertaking since the crack installers are increasing being used to push malware on installed devices.
Connected Home Monitor works with home networks as the name suggests. On public networks only a one-time scan is performed. As a result, you won't get notifications about new devices in public networks. Also a vulnerability scan is limited only to home networks.
Devices show up in circles depending on when they connected. There's no particular left-to-right order as far as I know.
If you run 2 scans in a row without any module update in between, the second scan will be significantly faster (unless you have a lot of archives on the disk). However, if modules are updated between the scans, the second scan will not be that quick since cached results from the first scan will be invalidated.