In official note from Dropbox here: https://blogs.dropbox.com/developers/2016/06/api-v1-deprecated/ it is stated that "we’ll be turning off API v1 a year from now, on 6/28/2017."
Does it mean that until 6/28/2017 dropbox api v1 will be still working ok? Or does it mean that they (dropbox) can disable dropbox api v1 any time until 6/28/2017 ?
Yes, Dropbox API v1 will continue working until June 28, 2017. A more detailed timeline is available at the bottom of the blog post.