Buttons bounding box: black dotted outline/borders visible - Indesign interactive PDF in Acrobat

The black dotted outline box that you are seeing is an Adobe Acrobat preferences setting (for each user). If you go to Edit > Preferences > Forms and uncheck the "Show Focus Rectangle" box, you will see that your issue resolves... However... That will only effect your Acrobat interface. The users you share the file with would also have to change their Preference settings in order not to see the black outlined box.

I'm not seeing black outlined buttons in your screen shots. Also, could you be specific as to how you've created the buttons and how you've made your interactive pdfs. Also, please be aware that Interactive pdfs made with elements from the Buttons and Forms Panel are only guaranteed to be read acurately using Acrobat version 9 or above. If you are testing using an earlier version of Acrobat then that could be the source of your problem. As you said, the aim is to have your pdfs read acurately by as many pdf viewers as possible. Unfortunately by its very nature that is not really possible. I'm actually surprised that Mac's Preview is reading them. I have not always found that to be the case.

Regarding buttons, you can have a word or words or an image (such as a button shape) as a document hyperlink to say another page in the document, or to an external website.
Some devices, for example, iPads, don't have rollover capability – only click – you should avoid multi-action buttons like On Click, On Roll Over, etc.  Multi-state objects (MSO) don’t work at all in Interactive PDFs.