If you have to use multiple screens then here’s a tutorial for sending data between screens:
http://community.thunkable.com/t/sending-more-than-one-start-value-to-another-screen/1312?u=domhnall
But I don’t really think you need two screens for this, as your app will be a lot slower having to go back aand forth between screens so often. Why not use your buttons to toggle the visibility of your listView? This way everything can be kept on the same screen.