I want to check two things
Found it! To find the bot's permissions, let's say, after a message (msg =>) was sent by a user:
CHANNEL permission:
msg.guild.me.permissionsIn(msg.channel).has(<permission string here>)
SERVER permission
msg.guild.me.hasPermission(<permission string here>)
LDinos' answer is correct for Discord.js v12. However, Discord.js v13 removed the hasPermission permission in favour of permissions.has.
Channel permissions:
msg.guild.me.permissionsIn(msg.channel).has(permissions)
Guild (server) permissions:
msg.guild.me.permissions.has(permissions)