The short answers to the things players actually ask.
Setup reads your collection log from the game and creates a local cache so the panel can open instantly. That stays on your computer. Web publishing is a separate opt-in: enable Kill Clog web sync to publish your collection log and personal bests. Publishing your profile-card appearance is another separate action inside the profile-card window.
Kill Clog can only display collection-log data a player has made available through Kill Clog, TempleOSRS, or RuneProfile. Their Jagex hiscores still work. Once they sync to one of those services, their colored log can appear when friends look them up.
Your local cache is a single file in .runelite/kill-clog, named after your character. Close RuneLite, delete that file, log into the main game, open your collection log, and run Setup again.
RuneLite shows that standard warning for every Plugin Hub plugin that connects to services outside Jagex or RuneLite. Player lookups may ask TempleOSRS, RuneProfile, Kill Clog, and the OSRS Wiki for data. Like any internet request, the service can see the IP address that made it. Kill Clog does not store request IPs as player-profile data.
!kclog <boss> posts your kill count and collection progress. !missing <boss> lists the drops you still need. !3a and !gilded show your treasure-trail rares. Boss shorthand works too, including !kclog cg and !kclog zammy.