Can I change an app's settings / press it's buttons ?
Standard Android doesn't allow an app to change, poke, prod or peek at anything within another app, including simulating keypresses and screen taps.
On the Cyanogen modified ROM, you can use some of the actions in the Input category to navigate around an app, click on UI elements and enter text automatically.
Can I control / respond to events in application X with Tasker ?
If a Tasker user wants to automate some aspect of another program they use, they just need to point the developer of the other app at the Tasker Developer Page and nag at him/her a bit.
The developer can in most cases very easily broadcast a message when something happens that Tasker should respond to ('an email arrived') and listen for a message that Tasker sends when the user wants it to do something ('switch to page X'). Tasker just needs to know the details of those messages.
It's in the developer's best interests to set this up if the competition have not done so.