Adding the bot
Discord only lets you add a bot where you have the Manage Server permission, so that is the short answer to which of your servers you can add it to.
The invite link asks for the exact permissions the bot's features need: reading and sending messages, embedding links, managing messages for the purge command, connecting and speaking in voice channels, timing members out, and managing roles. Discord shows you the full list on the authorisation screen before you accept.
Administrator is on that list too. It is there so the bot never hits a missing-permission wall on a server with unusual channel overrides — the most common complaint before it was added was the bot not seeing channels it had been given. It does mean the bot can do anything on your server, and Discord shows you that clearly before you accept.