Question Answer
Why isn't Auto-moderator deleting messages Following reasons:

1. Auto-moderator ignores moderators and administrators.
2. Tyche doesn't have the Manage messages permission
Why can users type/speak even if they have the muted role? It depends upon your channel perms. Configure your channel's send message permissions to be ticked for all the roles (which includes everyone role) and deny it for the muted role.
How do I unwarn a user? Note: You cannot clear individual warnings for a user
To clear all warnings do /clearwarns [User]
How do I unban/ban someone who is not in the server anymore? For bans:
You would use their ID; /ban [User ID]
For unbans:
Do the same thing; /unban [User ID]
Why can't Tyche purge messages older than 14 days? Due to Discord's limitations, bots on Discord cannot purge messages older than 14 days.