Answer one:
When using the reference set selector you are influancing the references between objects. Note that after selecting you have set the reference but it is not yet saved to the database. That will happen if you save your main object.
Answer two:
Select pages are a special set. The checkboxes are there to make it visual easier to see which options you have selected. You can modify the page to your own liking.
Answer three:
You can not. What you could to is already set references in a microflow before you show the main object. It would then already show those references and you can let the user still remove or add references.
Answer four:
Use a widget for that: https://appstore.home.mendix.com/link/app/2349/Mendix/Simple-Checkbox-Set-Selector
Hope this helps,
Regards,
Ronald
[EDIT]
The magic happens in the specific select buttons. So in the reference set selector you define the page where the objects can be selected and the select button makes the magic happen to set the right reference for those selected objects. You can create your own microflows and pages but that is quite some more work then using the auto generated pages.
The styling should be done on the select page. You can put the right classes on the objects there.