If you want your button to be visible / invisible depending on one value (your dropdown value), then you need to put that button in the same dataview as your dropdown, and put it’s visibility according to the value :
For your second question, you can add a text next to the dropdown (with some css you should be able to put it next to it), if you want the sign to appear inside the dropdown, I would probably change the dropdown enumeration to include the sign directly