You seem to have several different questions muddled together.
If you want your Arduino to detect rotational movement but not absolute position, you can use a rotary encoder. These can be set up to behave similar to a mouse wheel - you can tell when they have been turned and in which direction and how far, but they don't have any absolute position indication. Obviously there are numerous sources for momentary switches. You can even get rotary knobs with an integral pushbutton so that you push the knob to operate the button and turn it to operate the encoder. This seems like the sort of thing you need.