ATM if you want to find out as a simple user:
- the page syntax
- whether the page is hidden or not
- the page original language
- the missing page translations
you need to edit the page and look at the edit panels. This means you need to have edit right on the page to get this information. This is too restrictive. I don't see any reason why this information should not be available on the page Information tab since this tab is designed precisely for this.
Moreover, in the context of in-place editing (
XWIKI-17145), we should be able to edit this information (provided you have edit rights) directly from the Information tab. Note that all the other tabs are modifying the current page, so this is not unusual.