Hey @NLeVasseur,
Your Layout Builder setup is incorrect. To keep it simple at first, just add The Content element only. You can add additional elements when you already know how to use the Layout Builder.
Regarding the preview in the Layout Builder, you first need to Assign the layout to the events page that is not powered by Tribe Events. You only add the event shortcode to the page and that will be displayed by The Content element.
If you still don’t see the correct page preview, you can select it in the Layout Builder Preview Options.

You cannot edit The Content element. The Content element will display the content you insert in the WordPress Page Editor or content area so if you insert the event shortcode in the WordPress Page Editor, The Content element will display that in the Layout provided you assign the layout correctly.
Regarding showing the Month view, contact Tribe Events shortcode if there is a shortcode to display that. Again, you need to insert the shortcode in the WordPress Page Editor and The Content element will display that.
Thanks.