There are a few I found in Github here: https://github.com/topics/lemmy-bot. This one looks like it’s a pretty generic bot: https://github.com/SleeplessOne1917/lemmy-bot
There is an API for Lemmy, though the easiest way to make a bot would be to use one of the official libraries to talk to Lemmy: https://github.com/LemmyNet/lemmy#libraries
Hot and active are currently broken and will show stale content. It’s a Lemmy thing not a Jerboa thing. I’m hoping they fix this in the upcoming version that’s in testing right now.