I've tried multiple different times to register this account into Cheeseformice, each time when I get the registration code, and type the commands to Cfmbot in whisper, it says ''> [Cfmbot] Disconnected player''
I am logged in with this account when I send these messages.

In cheeseformice it shows that I have an account.

When I try to log in, this happens.

Help?

The first screenshot you've showed only shows that you have a Transformice account - not a CheeseForMice one. However as Cfmbot is currently disconnected as you've pointed out, you can't register through that method until the bot is fixed. You'll have to get in contact with a member of the CFM staff (by whispering them ingame, sending them a PM on these forums, etc.) to get your account confirmed and created there until the bot is fixed.