To answer your questions in the same order:
1. If you activate Run or Review mode after selecting a state value, that state value will be set when it opens the new window. This is to make testing different values easier. Reviewers who navigate between pages normally should not encounter this.
To avoid encountering this when you test the design, just click the Reset button in the right of the toolbar to make all the state values for the design default.
2. Since stateful component will always use the default state value when a design loads, you have two options to achieve what you are looking for. You can either add in a real default value (Usually called Off or None) that is not associated with any of the other components or you can use another set of radio buttons to simulate the radio buttons to be unselected.
To create the second option, you'll need to have a set of text radio buttons that you place at the same position of your stateful radio button group. You would want a text radio button for each value you have and have them named after the values.
You will then create a single state that lets you hide your stateful radio button group when any of the text buttons is clicked. You will also need each individual text radio to change the state to the value it displays. This will make it look like it is the same group of radio buttons and allow you to have nothing selected by default.
3. If you use textful radio buttons you can have each individual button activate/change a different state. If your radio buttons are stateful, it will deploy each value as an option and it is not possible to control an individual option. You would need to separate it from the group.
If you have any questions, please let us know.