Turn shortcuts on first. On the web, open Settings, then See all settings, then General, set Keyboard shortcuts to on, and save. Single-key actions like c, e, and r do nothing until this is enabled.
Send. Cmd+Enter sends the current message.
Compose and formatting use Cmd. Cmd+K inserts a link, Cmd+B, Cmd+I, and Cmd+U handle bold, italic, and underline, and Cmd+Shift with a number or letter covers fonts, lists, alignment, and quoting.
Inbox actions are single keys. e archives, # deletes, r replies, a replies all, f forwards, s stars, and x selects a conversation.
Jumping uses g. Press g then i for the inbox, g then s for starred, g then t for sent, and g then d for drafts. Press the keys in sequence.
Chat navigation uses Ctrl. Ctrl and period or Ctrl and comma move between chat and compose windows, one of the few places Gmail on Mac uses Ctrl rather than Cmd. The full set is in the table above.