Is it possible to check somehow whether user is logged in or not from theme front-end?
It’s Not Possible In Ghost At Present But You Can Private Your Blog.
Ghost’s admin panel is an entirely separate app to the site that is rendered with your theme. If you are logged in via the admin panel (or Ghost desktop) there’s absolutely no way for the theme to know about this.
There are however a bunch of shortcut URLs. If you’re on a post and you want to edit it, type
/edit/ on the end of the URL and if you’re logged in the editor will load. The same thing works on tag and author pages.