Yes, if you selected both it will save all the settings available from both tabs.

You can share any preset you made, all you have to do is go to the presets folder you have set and share the .json files, and the other person can put it in their presets folder and click refresh.

Yes, you can select which you want to save, or you can save both

Yes, you can create a new blend file after enabling the addon you can select the previous folder you have saved your presets on, click refresh and you should be able to load it.