Here are the solutions on your queries:
1. The Customize Options only shows the widgets which are available for those pages. So, for the Magazine Sidebar to appear in the Customize Options, can you create an empty page in your site via the Magazine Template chosen for it? After that, if you navigate to the same page via the Customize Options, then, those Magazine Sidebar areas will get displayed on it.
Note: You can also manage the widgets via Appearance->Widgets section. So, can you check on that?
2. It probably looks like it is due to the used plugin in your site. So, can you deactivate the used plugins in your site and check? Also, if you could provide the link to your site, then, probably I could have a look on this and provide you with the required solution on this if possible.