I really do not understand what this bot system is and what bots are, can someone explain it to me?
Also, is BOT LeelaChess a person? I want to challenge her/him but sometimes they are not online and sometimes they don't accept the challenge.
A bot will typically be a remote chess engine running on its owner's computer. It might be left running online unattended, or it might just be online when the owner is there monitoring it, e.g the owner might be the author testing a new version and ready to take it offline if it crashes.
Leela is a chess program which learns from crowd sourced data so there might be many copies of the engine running here when enough volunteers have bot accounts.
So there is no guarantee that a bot will be online. If it is online and you issue a challenge, the bot could be busy playing another game, or it might refuse to play because it wants games with particular time controls, opponent rating, rated/unrated games, black/white/random color, etc.
Over time it will probably become easier to run a bot on lichess and we can expect to see some regular bots almost permanently online and some competition to have the highest rated bots by a mixture of programming skills and cloning and buying bigger and better hardware!