I have an interface (android activity, but that should not matter) with text input, spinners and a toggle button (all on one page). Depending on the state of all these elements I produce text output (on the same page).
Since the relationship is not trivial, I would like to somehow visualize the logic relationship between these elements. I am reading about UML, activity diagrams, etc but got a bit lost there.
What term should I look for? What program do you recommend to use for drawing such diagrams on computer (linux)?
UML Activity Diagrams might not be what you are looking for. They are usually used to model activities in a process. They tend to be more high-level and conceptual and less about the implementation.
From your question it reads as if you are working on the implementation itself. In that case I would urge you to look at UML State Diagrams. They are really neat when you want to think about different states your application (or components of your application) can be in. It also lets you logically decompose behaviour into states.
Furthermore, it is also a straight-forward way to model your application in a way that you can apply a Design Pattern, notably the State Pattern, to implement your model.