Q:

TYPO3 Extbase - How to call a controller action from external

Lets say I have an extension called my_extension and in the my_extension a plugin called apiResponse.
Then I have in my controller a function called sendApiDataAction.
How can I call this sendApiDataAction from external via a usual http GET request?

A:

First, you need these information from your extension:

extensionKey (that's easy, in your example it's myExtension)
pluginName (that's the name you defined in your ext_localconf.php where you assign the actions)
actionName (in your example sendApiData - without the action)
controllerName (that's the controller where your action is)
pageId (that's the page id where your plugin is implemented)
namespace (that's a name built from your plugin and your extension, in your case tx_myextension_{pluginName}

Then, you can access the action by 
http(s)://your.domain.tld/index.php?id={pageId}&{namespace}[controller]={controllerName}&{namespace}[action]={actionName}

