Ten useful shortcuts while using terminator:
CTRL + SHIFT + E : Open another instance adjacent to the one you have, but withou openning a new window. Usefull when you wanna send several commands and hava a one galnce view to all.
CTRL + SHIFT + T : Open another instance in a new tab of the same window.
CTRL + SHIFT + W : Closes an instance.
ALT + A : Broadcast to all tabs of terminator
ALT + G : Broadcast to the group of the selected tab
ALT + O : Turn off broadcast
SUPER + G : Group all windows
SHIFT + SUPER + G : Ungroup all windows
CTRL + SHIFT + X : Toggle between one tab terminal and all tabs.
ALT + F2 : Run a command
Though one thing terminator lacks is how to open an new terminator window while establishing a new ssh connection to a remote host. You can indeed, achieve that with profiles but if you have dozens of remote servers, it can become hard to manage.
In this case consider using tmux.