Firstly, any questions about interaction with Tasker, please use the Developer board.
Run External Actions
The preferred way to trigger external actions from Tasker is to write an action plugin which will then appear in the Plugins action category.
A simpler way is to use the existing AutoShare plugin. This method is quicker but less flexible and requires AutoShare to be installed.
If those are of the question, you could make your component controllable via intent broadcasts and contact the developer via the Developer board. Your app can then be included in the 3rd Party action category.
No guarantees are made about which apps will be included in this manner so please contact the developer before you do any work in this direction.
Signal Tasker That Something Has Happened
Again, the preferred method is to write a condition or event plugin which will then appear in the Plugin state or event category.
If you feel a condition or event plugin is not suitable for your purpose, then the developer may consider including an intent handler for it which will then appear as an Event or a State, depending what's most appropriate.
Just make a post on the Developer board with the details ('I broadcast x.y.ACTION_X when X happens, it has these extras...').
Finally, Tasker also offers the event Intent Received, you could give your users the details they need
to fill in the parameters for that event.
Run Existing and New Tasks
You can easily create tasks programatically for Tasker to run, or invoke named tasks previously created
by the user. For more information see here.
Home Screen Intent
Tasker's Go Home action can specify the page of the home screen which should be shown. To support this action, a home screen need only accept the extra
with the launch intent, the value being an integer from 1 to 20.
Tasker's ContentProvider serves some data which may
be useful to external apps.