There is no way to use contextual links on mobile devices at the moment, because they are only triggered by hovering your mouse over the editable/configurable items, and mobile devices work with taps.
In D8, they have added an "Edit" button at the far right of the admin bar, that toggles contextual links on/off:

We should have the same.
GitHub Issue #:
3417
Recent comments
Worth mentioning as it was in zulip chat by @yorkshirepudding I just tested and the two work together without issue as long as you don't use the "Exclude comments from Content...
Search does not include comments
There is also Node Comments Search - this searches the node and all comments (default search is node and first page of comments) as part of the content search. Izzy's module above is a separate...
Search does not include comments
I have created a new module comment_search
Search does not include comments