Channel operators

When you're an operator, right-click someone in the cast for Give/Take operator, Give/Take voice, Quiet, Kick, Ban and Kick and Ban. The same is there as commands:

Command
/kick nick [reason]	Kicks someone. Alias /k.
/ban nick or /ban mask	Bans someone.
/kickban nick [reason]	Bans, then kicks, so they can't rejoin in between. Alias /kb.
/quiet nick / /unquiet nick	Silences someone without kicking them.
/banlist / /quietlist	Lists the channel's bans or quiets.
/op, /deop, /voice, /devoice nick…	Several nicks at once, grouped as the server allows.
/halfop, /dehalfop nick…	Where the network has half-operators.
/topic text	Sets the topic.
/invite nick	Invites someone here.
/mode +m	Any other mode.

Bans by host

Given a nick, /ban, /kickban and /quiet ban *!*@host when Keryx knows the person's host (from the member list), so a new nick doesn't get round the ban. If the host isn't known, they fall back to nick!*@*. A mask with !, @ or * is used as you wrote it.

Quiets on each network

Networks silence people in different ways. Keryx reads the server's CHANMODES and EXTBAN and picks the right one:

• Libera, OFTC and other Solanum/Charybdis networks: the +q list.
• UnrealIRCd: the ~q: extban.
• InspIRCd: the m: extban.
• Ergo and others without either: /quiet explains instead; use +m and voice.

Lists

Replies to /banlist, /quietlist, and /mode +e or +I appear as readable lines in the channel — mask, who set it and when — ending with a count, or "No bans" when empty.